Math / Algebra

QuestionSolve the inequallity. Graph your solution.
9. $\frac{x}{-10} \leq 22$
13. $1.6 x \leq-11.2$
17. $\frac{x}{1.3} \geq 7.1$
21. $-0.1 x \leq-2.5$
22. $-9.8 x \geq 44.1$
11. $-13 x<-208$
15. $-10.7>\frac{x}{-4}$
19. $-3.8 x \geq 28.5$
23. $\frac{x}{-12.7} \geq-2.2$
12. $45 x \leq-855$
16. $8.3 \leq \frac{x}{-5}$
20. $10.4 x>520$
24. $\frac{x}{4.2}<-20.45$

Studdy Solution

STEP 1

1. We are solving linear inequalities for the variable $x$ .
2. The inequalities involve basic algebraic operations, specifically multiplication and division.
3. When multiplying or dividing both sides of an inequality by a negative number, the inequality sign must be reversed.
4. We will graph the solution on a number line for each inequality.

STEP 2

1. Solve each inequality for $x$ .
2. Graph the solution on a number line.

STEP 3

Solve the inequality $\frac{x}{-10} \leq 22$ .
Multiply both sides by $-10$ and reverse the inequality sign:
$x \geq 22 \times (-10)$ $x \geq -220$

STEP 4

Graph the solution $x \geq -220$ on a number line.
Draw a number line, place a closed circle at $-220$ , and shade to the right.

STEP 5

Solve the inequality $1.6x \leq -11.2$ .
Divide both sides by $1.6$ :
$x \leq \frac{-11.2}{1.6}$ $x \leq -7$

STEP 6

Graph the solution $x \leq -7$ on a number line.
Draw a number line, place a closed circle at $-7$ , and shade to the left.

STEP 7

Solve the inequality $\frac{x}{1.3} \geq 7.1$ .
Multiply both sides by $1.3$ :
$x \geq 7.1 \times 1.3$ $x \geq 9.23$

STEP 8

Graph the solution $x \geq 9.23$ on a number line.
Draw a number line, place a closed circle at $9.23$ , and shade to the right.

STEP 9

Solve the inequality $-0.1x \leq -2.5$ .
Divide both sides by $-0.1$ and reverse the inequality sign:
$x \geq \frac{-2.5}{-0.1}$ $x \geq 25$

STEP 10

Graph the solution $x \geq 25$ on a number line.
Draw a number line, place a closed circle at $25$ , and shade to the right.

STEP 11

Solve the inequality $-9.8x \geq 44.1$ .
Divide both sides by $-9.8$ and reverse the inequality sign:
$x \leq \frac{44.1}{-9.8}$ $x \leq -4.5$

STEP 12

Graph the solution $x \leq -4.5$ on a number line.
Draw a number line, place a closed circle at $-4.5$ , and shade to the left.

STEP 13

Solve the inequality $-13x < -208$ .
Divide both sides by $-13$ and reverse the inequality sign:
$x > \frac{-208}{-13}$ $x > 16$

STEP 14

Graph the solution $x > 16$ on a number line.
Draw a number line, place an open circle at $16$ , and shade to the right.

STEP 15

Solve the inequality $-10.7 > \frac{x}{-4}$ .
Multiply both sides by $-4$ and reverse the inequality sign:
$x < -10.7 \times (-4)$ $x < 42.8$

STEP 16

Graph the solution $x < 42.8$ on a number line.
Draw a number line, place an open circle at $42.8$ , and shade to the left.

STEP 17

Solve the inequality $-3.8x \geq 28.5$ .
Divide both sides by $-3.8$ and reverse the inequality sign:
$x \leq \frac{28.5}{-3.8}$ $x \leq -7.5$

STEP 18

Graph the solution $x \leq -7.5$ on a number line.
Draw a number line, place a closed circle at $-7.5$ , and shade to the left.

STEP 19

Solve the inequality $\frac{x}{-12.7} \geq -2.2$ .
Multiply both sides by $-12.7$ and reverse the inequality sign:
$x \leq -2.2 \times (-12.7)$ $x \leq 27.94$

STEP 20

Graph the solution $x \leq 27.94$ on a number line.
Draw a number line, place a closed circle at $27.94$ , and shade to the left.

STEP 21

Solve the inequality $45x \leq -855$ .
Divide both sides by $45$ :
$x \leq \frac{-855}{45}$ $x \leq -19$

STEP 22

Graph the solution $x \leq -19$ on a number line.
Draw a number line, place a closed circle at $-19$ , and shade to the left.

STEP 23

Solve the inequality $8.3 \leq \frac{x}{-5}$ .
Multiply both sides by $-5$ and reverse the inequality sign:
$x \geq 8.3 \times (-5)$ $x \geq -41.5$

STEP 24

Graph the solution $x \geq -41.5$ on a number line.
Draw a number line, place a closed circle at $-41.5$ , and shade to the right.

STEP 25

Solve the inequality $10.4x > 520$ .
Divide both sides by $10.4$ :
$x > \frac{520}{10.4}$ $x > 50$

STEP 26

Graph the solution $x > 50$ on a number line.
Draw a number line, place an open circle at $50$ , and shade to the right.

STEP 27

Solve the inequality $\frac{x}{4.2} < -20.45$ .
Multiply both sides by $4.2$ :
$x < -20.45 \times 4.2$ $x < -85.89$

STEP 28

Graph the solution $x < -85.89$ on a number line.
Draw a number line, place an open circle at $-85.89$ , and shade to the left.

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Studdy Solution

STEP 1

STEP 2

1. Solve each inequality for x x x.2. Graph the solution on a number line.

STEP 3

Solve the inequality x−10≤22 \frac{x}{-10} \leq 22 −10x​≤22.Multiply both sides by −10-10−10 and reverse the inequality sign:x≥22×(−10) x \geq 22 \times (-10) x≥22×(−10) x≥−220 x \geq -220 x≥−220

STEP 4

Graph the solution x≥−220 x \geq -220 x≥−220 on a number line.Draw a number line, place a closed circle at −220-220−220, and shade to the right.

STEP 5

Solve the inequality 1.6x≤−11.2 1.6x \leq -11.2 1.6x≤−11.2.Divide both sides by 1.6 1.6 1.6:x≤−11.21.6 x \leq \frac{-11.2}{1.6} x≤1.6−11.2​ x≤−7 x \leq -7 x≤−7

STEP 6

Graph the solution x≤−7 x \leq -7 x≤−7 on a number line.Draw a number line, place a closed circle at −7-7−7, and shade to the left.

STEP 7

Solve the inequality x1.3≥7.1 \frac{x}{1.3} \geq 7.1 1.3x​≥7.1.Multiply both sides by 1.3 1.3 1.3:x≥7.1×1.3 x \geq 7.1 \times 1.3 x≥7.1×1.3 x≥9.23 x \geq 9.23 x≥9.23

STEP 8

Graph the solution x≥9.23 x \geq 9.23 x≥9.23 on a number line.Draw a number line, place a closed circle at 9.239.239.23, and shade to the right.

STEP 9

Solve the inequality −0.1x≤−2.5 -0.1x \leq -2.5 −0.1x≤−2.5.Divide both sides by −0.1-0.1−0.1 and reverse the inequality sign:x≥−2.5−0.1 x \geq \frac{-2.5}{-0.1} x≥−0.1−2.5​ x≥25 x \geq 25 x≥25

STEP 10

Graph the solution x≥25 x \geq 25 x≥25 on a number line.Draw a number line, place a closed circle at 252525, and shade to the right.

STEP 11

Solve the inequality −9.8x≥44.1 -9.8x \geq 44.1 −9.8x≥44.1.Divide both sides by −9.8-9.8−9.8 and reverse the inequality sign:x≤44.1−9.8 x \leq \frac{44.1}{-9.8} x≤−9.844.1​ x≤−4.5 x \leq -4.5 x≤−4.5

STEP 12

Graph the solution x≤−4.5 x \leq -4.5 x≤−4.5 on a number line.Draw a number line, place a closed circle at −4.5-4.5−4.5, and shade to the left.

STEP 13

Solve the inequality −13x<−208 -13x < -208 −13x<−208.Divide both sides by −13-13−13 and reverse the inequality sign:x>−208−13 x > \frac{-208}{-13} x>−13−208​ x>16 x > 16 x>16

STEP 14

Graph the solution x>16 x > 16 x>16 on a number line.Draw a number line, place an open circle at 161616, and shade to the right.

STEP 15

Solve the inequality −10.7>x−4 -10.7 > \frac{x}{-4} −10.7>−4x​.Multiply both sides by −4-4−4 and reverse the inequality sign:x<−10.7×(−4) x < -10.7 \times (-4) x<−10.7×(−4) x<42.8 x < 42.8 x<42.8

STEP 16

Graph the solution x<42.8 x < 42.8 x<42.8 on a number line.Draw a number line, place an open circle at 42.842.842.8, and shade to the left.

STEP 17

Solve the inequality −3.8x≥28.5 -3.8x \geq 28.5 −3.8x≥28.5.Divide both sides by −3.8-3.8−3.8 and reverse the inequality sign:x≤28.5−3.8 x \leq \frac{28.5}{-3.8} x≤−3.828.5​ x≤−7.5 x \leq -7.5 x≤−7.5

STEP 18

Graph the solution x≤−7.5 x \leq -7.5 x≤−7.5 on a number line.Draw a number line, place a closed circle at −7.5-7.5−7.5, and shade to the left.

STEP 19

Solve the inequality x−12.7≥−2.2 \frac{x}{-12.7} \geq -2.2 −12.7x​≥−2.2.Multiply both sides by −12.7-12.7−12.7 and reverse the inequality sign:x≤−2.2×(−12.7) x \leq -2.2 \times (-12.7) x≤−2.2×(−12.7) x≤27.94 x \leq 27.94 x≤27.94

STEP 20

Graph the solution x≤27.94 x \leq 27.94 x≤27.94 on a number line.Draw a number line, place a closed circle at 27.9427.9427.94, and shade to the left.

STEP 21

Solve the inequality 45x≤−855 45x \leq -855 45x≤−855.Divide both sides by 454545:x≤−85545 x \leq \frac{-855}{45} x≤45−855​ x≤−19 x \leq -19 x≤−19

STEP 22

Graph the solution x≤−19 x \leq -19 x≤−19 on a number line.Draw a number line, place a closed circle at −19-19−19, and shade to the left.

STEP 23

Solve the inequality 8.3≤x−5 8.3 \leq \frac{x}{-5} 8.3≤−5x​.Multiply both sides by −5-5−5 and reverse the inequality sign:x≥8.3×(−5) x \geq 8.3 \times (-5) x≥8.3×(−5) x≥−41.5 x \geq -41.5 x≥−41.5

STEP 24

Graph the solution x≥−41.5 x \geq -41.5 x≥−41.5 on a number line.Draw a number line, place a closed circle at −41.5-41.5−41.5, and shade to the right.

STEP 25

Solve the inequality 10.4x>520 10.4x > 520 10.4x>520.Divide both sides by 10.410.410.4:x>52010.4 x > \frac{520}{10.4} x>10.4520​ x>50 x > 50 x>50

STEP 26

Graph the solution x>50 x > 50 x>50 on a number line.Draw a number line, place an open circle at 505050, and shade to the right.

STEP 27

Solve the inequality x4.2<−20.45 \frac{x}{4.2} < -20.45 4.2x​<−20.45.Multiply both sides by 4.24.24.2:x<−20.45×4.2 x < -20.45 \times 4.2 x<−20.45×4.2 x<−85.89 x < -85.89 x<−85.89

STEP 28

Graph the solution x<−85.89 x < -85.89 x<−85.89 on a number line.Draw a number line, place an open circle at −85.89-85.89−85.89, and shade to the left.

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1. Solve each inequality for $x$ .
2. Graph the solution on a number line.

Solve the inequality $\frac{x}{-10} \leq 22$ .
Multiply both sides by $-10$ and reverse the inequality sign:
$x \geq 22 \times (-10)$ $x \geq -220$

Graph the solution $x \geq -220$ on a number line.
Draw a number line, place a closed circle at $-220$ , and shade to the right.

Solve the inequality $1.6x \leq -11.2$ .
Divide both sides by $1.6$ :
$x \leq \frac{-11.2}{1.6}$ $x \leq -7$

Graph the solution $x \leq -7$ on a number line.
Draw a number line, place a closed circle at $-7$ , and shade to the left.

Solve the inequality $\frac{x}{1.3} \geq 7.1$ .
Multiply both sides by $1.3$ :
$x \geq 7.1 \times 1.3$ $x \geq 9.23$

Graph the solution $x \geq 9.23$ on a number line.
Draw a number line, place a closed circle at $9.23$ , and shade to the right.

Solve the inequality $-0.1x \leq -2.5$ .
Divide both sides by $-0.1$ and reverse the inequality sign:
$x \geq \frac{-2.5}{-0.1}$ $x \geq 25$

Graph the solution $x \geq 25$ on a number line.
Draw a number line, place a closed circle at $25$ , and shade to the right.

Solve the inequality $-9.8x \geq 44.1$ .
Divide both sides by $-9.8$ and reverse the inequality sign:
$x \leq \frac{44.1}{-9.8}$ $x \leq -4.5$

Graph the solution $x \leq -4.5$ on a number line.
Draw a number line, place a closed circle at $-4.5$ , and shade to the left.

Solve the inequality $-13x < -208$ .
Divide both sides by $-13$ and reverse the inequality sign:
$x > \frac{-208}{-13}$ $x > 16$

Graph the solution $x > 16$ on a number line.
Draw a number line, place an open circle at $16$ , and shade to the right.

Solve the inequality $-10.7 > \frac{x}{-4}$ .
Multiply both sides by $-4$ and reverse the inequality sign:
$x < -10.7 \times (-4)$ $x < 42.8$

Graph the solution $x < 42.8$ on a number line.
Draw a number line, place an open circle at $42.8$ , and shade to the left.

Solve the inequality $-3.8x \geq 28.5$ .
Divide both sides by $-3.8$ and reverse the inequality sign:
$x \leq \frac{28.5}{-3.8}$ $x \leq -7.5$

Graph the solution $x \leq -7.5$ on a number line.
Draw a number line, place a closed circle at $-7.5$ , and shade to the left.

Solve the inequality $\frac{x}{-12.7} \geq -2.2$ .
Multiply both sides by $-12.7$ and reverse the inequality sign:
$x \leq -2.2 \times (-12.7)$ $x \leq 27.94$

Graph the solution $x \leq 27.94$ on a number line.
Draw a number line, place a closed circle at $27.94$ , and shade to the left.

Solve the inequality $45x \leq -855$ .
Divide both sides by $45$ :
$x \leq \frac{-855}{45}$ $x \leq -19$

Graph the solution $x \leq -19$ on a number line.
Draw a number line, place a closed circle at $-19$ , and shade to the left.

Solve the inequality $8.3 \leq \frac{x}{-5}$ .
Multiply both sides by $-5$ and reverse the inequality sign:
$x \geq 8.3 \times (-5)$ $x \geq -41.5$

Graph the solution $x \geq -41.5$ on a number line.
Draw a number line, place a closed circle at $-41.5$ , and shade to the right.

Solve the inequality $10.4x > 520$ .
Divide both sides by $10.4$ :
$x > \frac{520}{10.4}$ $x > 50$

Graph the solution $x > 50$ on a number line.
Draw a number line, place an open circle at $50$ , and shade to the right.

Solve the inequality $\frac{x}{4.2} < -20.45$ .
Multiply both sides by $4.2$ :
$x < -20.45 \times 4.2$ $x < -85.89$

Graph the solution $x < -85.89$ on a number line.
Draw a number line, place an open circle at $-85.89$ , and shade to the left.