QuestionSolve the inequality $\frac{x-5}{4}+\frac{3-2 x}{3}<-2$ .

Studdy Solution

STEP 1

Assumptions1. We are given the inequality $\frac{x-5}{4}+\frac{3- x}{3}<-$ . We have to solve this inequality for x

STEP 2

To make the inequality easier to handle, we will first get rid of the fractions. We can do this by multiplying every term by the least common multiple (LCM) of the denominators. The LCM of4 and is12.
$12 \cdot \frac{x-5}{4}+12 \cdot \frac{-2 x}{} < -2 \cdot12$

STEP 3

implify the inequality by performing the multiplication.
$3(x-5) +(3-2x) < -24$

STEP 4

Expand the brackets.
$3x -15 +12 -8x < -24$

STEP 5

Combine like terms.
$-5x -3 < -24$

STEP 6

Add3 to both sides of the inequality to isolate the term with x on one side.
$-5x < -21$

STEP 7

Finally, divide both sides by -5 to solve for x. Remember, when you divide or multiply an inequality by a negative number, the direction of the inequality sign changes.
$x > \frac{21}{5}$ So, the solution to the inequality is $x > \frac{21}{5}$ or $x >4.2$ .

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QuestionSolve the inequality $\frac{x-5}{4}+\frac{3-2 x}{3}<-2$ .

Studdy Solution

STEP 1

Assumptions1. We are given the inequality $\frac{x-5}{4}+\frac{3- x}{3}<-$ . We have to solve this inequality for x

STEP 2

To make the inequality easier to handle, we will first get rid of the fractions. We can do this by multiplying every term by the least common multiple (LCM) of the denominators. The LCM of4 and is12.
$12 \cdot \frac{x-5}{4}+12 \cdot \frac{-2 x}{} < -2 \cdot12$

STEP 3

implify the inequality by performing the multiplication.
$3(x-5) +(3-2x) < -24$

STEP 4

Expand the brackets.
$3x -15 +12 -8x < -24$

STEP 5

Combine like terms.
$-5x -3 < -24$

STEP 6

Add3 to both sides of the inequality to isolate the term with x on one side.
$-5x < -21$

STEP 7

Finally, divide both sides by -5 to solve for x. Remember, when you divide or multiply an inequality by a negative number, the direction of the inequality sign changes.
$x > \frac{21}{5}$ So, the solution to the inequality is $x > \frac{21}{5}$ or $x >4.2$ .

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QuestionSolve the inequality x−54+3−2x3<−2\frac{x-5}{4}+\frac{3-2 x}{3}<-24x−5​+33−2x​<−2.

Studdy Solution

STEP 1

Assumptions1. We are given the inequality x−54+3−x3<−\frac{x-5}{4}+\frac{3- x}{3}<-4x−5​+33−x​<− . We have to solve this inequality for x

STEP 2

STEP 3

implify the inequality by performing the multiplication.3(x−5)+(3−2x)<−243(x-5) +(3-2x) < -243(x−5)+(3−2x)<−24

STEP 4

Expand the brackets.3x−15+12−8x<−243x -15 +12 -8x < -243x−15+12−8x<−24

STEP 5

Combine like terms.−5x−3<−24-5x -3 < -24−5x−3<−24

STEP 6

Add3 to both sides of the inequality to isolate the term with x on one side.−5x<−21-5x < -21−5x<−21

STEP 7

Finally, divide both sides by -5 to solve for x. Remember, when you divide or multiply an inequality by a negative number, the direction of the inequality sign changes.x>215x > \frac{21}{5}x>521​So, the solution to the inequality is x>215x > \frac{21}{5}x>521​ or x>4.2x >4.2x>4.2.

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QuestionSolve the inequality $\frac{x-5}{4}+\frac{3-2 x}{3}<-2$ .

Assumptions1. We are given the inequality $\frac{x-5}{4}+\frac{3- x}{3}<-$ . We have to solve this inequality for x

implify the inequality by performing the multiplication.
$3(x-5) +(3-2x) < -24$

Expand the brackets.
$3x -15 +12 -8x < -24$

Combine like terms.
$-5x -3 < -24$

Add3 to both sides of the inequality to isolate the term with x on one side.
$-5x < -21$

Finally, divide both sides by -5 to solve for x. Remember, when you divide or multiply an inequality by a negative number, the direction of the inequality sign changes.
$x > \frac{21}{5}$ So, the solution to the inequality is $x > \frac{21}{5}$ or $x >4.2$ .