QuestionSolve the inequalities $\frac{4 d+7}{3}>5$ or $-3 d+4 \geq 19$ . Plot endpoints, change one from closed to open, and delete a middle segment.

Studdy Solution

STEP 1

Assumptions1. We are given two inequalities $\frac{4d +7}{3} >5$ and $-3d +4 \geq19$ . . We need to solve each inequality for $d$ .
3. We will plot the solutions on a number line.

STEP 2

Let's start by solving the first inequality $\frac{4d +7}{} >5$ for $d$ . We can do this by first multiplying both sides of the inequality by to remove the denominator.
$\times \frac{4d +7}{} > \times5$

STEP 3

implify the left side of the inequality to get $d +7$ and the right side to get $15$ .
$d +7 >15$

STEP 4

Next, subtract7 from both sides of the inequality to isolate $4d$ on the left side.
$4d +7 -7 >15 -7$

STEP 5

implify the inequality to get $4d >8$ .
$4d >8$

STEP 6

Finally, divide both sides of the inequality by4 to solve for $d$ .
$\frac{4d}{4} > \frac{8}{4}$

STEP 7

implify the inequality to get $d >2$ .
$d >2$

STEP 8

Now let's solve the second inequality $-3d +4 \geq19$ for $d$ . We can start by subtracting4 from both sides of the inequality to isolate $-3d$ on the left side.
$-3d +4 -4 \geq19 -4$

STEP 9

implify the inequality to get $-3d \geq15$ .
$-3d \geq15$

STEP 10

Next, divide both sides of the inequality by -3 to solve for $d$ . Remember that when we divide or multiply an inequality by a negative number, we must reverse the direction of the inequality sign.
$\frac{-3d}{-3} \leq \frac{15}{-3}$

STEP 11

implify the inequality to get $d \leq -5$ .
$d \leq -5$

STEP 12

Now we have the solutions to the two inequalities $d >2$ and $d \leq -5$ . We can plot these on a number line. The number line should have an open circle at2 and a closed circle at -5. The line should extend to the right from2 and to the left from -5.

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QuestionSolve the inequalities $\frac{4 d+7}{3}>5$ or $-3 d+4 \geq 19$ . Plot endpoints, change one from closed to open, and delete a middle segment.

Studdy Solution

STEP 1

Assumptions1. We are given two inequalities $\frac{4d +7}{3} >5$ and $-3d +4 \geq19$ . . We need to solve each inequality for $d$ .
3. We will plot the solutions on a number line.

STEP 2

Let's start by solving the first inequality $\frac{4d +7}{} >5$ for $d$ . We can do this by first multiplying both sides of the inequality by to remove the denominator.
$\times \frac{4d +7}{} > \times5$

STEP 3

implify the left side of the inequality to get $d +7$ and the right side to get $15$ .
$d +7 >15$

STEP 4

Next, subtract7 from both sides of the inequality to isolate $4d$ on the left side.
$4d +7 -7 >15 -7$

STEP 5

implify the inequality to get $4d >8$ .
$4d >8$

STEP 6

Finally, divide both sides of the inequality by4 to solve for $d$ .
$\frac{4d}{4} > \frac{8}{4}$

STEP 7

implify the inequality to get $d >2$ .
$d >2$

STEP 8

Now let's solve the second inequality $-3d +4 \geq19$ for $d$ . We can start by subtracting4 from both sides of the inequality to isolate $-3d$ on the left side.
$-3d +4 -4 \geq19 -4$

STEP 9

implify the inequality to get $-3d \geq15$ .
$-3d \geq15$

STEP 10

Next, divide both sides of the inequality by -3 to solve for $d$ . Remember that when we divide or multiply an inequality by a negative number, we must reverse the direction of the inequality sign.
$\frac{-3d}{-3} \leq \frac{15}{-3}$

STEP 11

implify the inequality to get $d \leq -5$ .
$d \leq -5$

STEP 12

Now we have the solutions to the two inequalities $d >2$ and $d \leq -5$ . We can plot these on a number line. The number line should have an open circle at2 and a closed circle at -5. The line should extend to the right from2 and to the left from -5.

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QuestionSolve the inequalities 4d+73>5\frac{4 d+7}{3}>534d+7​>5 or −3d+4≥19-3 d+4 \geq 19−3d+4≥19. Plot endpoints, change one from closed to open, and delete a middle segment.

Studdy Solution

STEP 1

Assumptions1. We are given two inequalities 4d+73>5\frac{4d +7}{3} >534d+7​>5 and −3d+4≥19-3d +4 \geq19−3d+4≥19. . We need to solve each inequality for ddd.3. We will plot the solutions on a number line.

STEP 2

Let's start by solving the first inequality 4d+7>5\frac{4d +7}{} >54d+7​>5 for ddd. We can do this by first multiplying both sides of the inequality by to remove the denominator.×4d+7>×5 \times \frac{4d +7}{} > \times5×4d+7​>×5

STEP 3

implify the left side of the inequality to get d+7d +7d+7 and the right side to get 151515.d+7>15d +7 >15d+7>15

STEP 4

Next, subtract7 from both sides of the inequality to isolate 4d4d4d on the left side.4d+7−7>15−74d +7 -7 >15 -74d+7−7>15−7

STEP 5

implify the inequality to get 4d>84d >84d>8.4d>84d >84d>8

STEP 6

Finally, divide both sides of the inequality by4 to solve for ddd.4d4>84\frac{4d}{4} > \frac{8}{4}44d​>48​

STEP 7

implify the inequality to get d>2d >2d>2.d>2d >2d>2

STEP 8

Now let's solve the second inequality −3d+4≥19-3d +4 \geq19−3d+4≥19 for ddd. We can start by subtracting4 from both sides of the inequality to isolate −3d-3d−3d on the left side.−3d+4−4≥19−4-3d +4 -4 \geq19 -4−3d+4−4≥19−4

STEP 9

implify the inequality to get −3d≥15-3d \geq15−3d≥15.−3d≥15-3d \geq15−3d≥15

STEP 10

Next, divide both sides of the inequality by -3 to solve for ddd. Remember that when we divide or multiply an inequality by a negative number, we must reverse the direction of the inequality sign.−3d−3≤15−3\frac{-3d}{-3} \leq \frac{15}{-3}−3−3d​≤−315​

STEP 11

implify the inequality to get d≤−5d \leq -5d≤−5.d≤−5d \leq -5d≤−5

STEP 12

Now we have the solutions to the two inequalities d>2d >2d>2 and d≤−5d \leq -5d≤−5. We can plot these on a number line. The number line should have an open circle at2 and a closed circle at -5. The line should extend to the right from2 and to the left from -5.

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Studdy solves anything!

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

QuestionSolve the inequalities $\frac{4 d+7}{3}>5$ or $-3 d+4 \geq 19$ . Plot endpoints, change one from closed to open, and delete a middle segment.

Assumptions1. We are given two inequalities $\frac{4d +7}{3} >5$ and $-3d +4 \geq19$ . . We need to solve each inequality for $d$ .
3. We will plot the solutions on a number line.

Let's start by solving the first inequality $\frac{4d +7}{} >5$ for $d$ . We can do this by first multiplying both sides of the inequality by to remove the denominator.
$\times \frac{4d +7}{} > \times5$

implify the left side of the inequality to get $d +7$ and the right side to get $15$ .
$d +7 >15$

Next, subtract7 from both sides of the inequality to isolate $4d$ on the left side.
$4d +7 -7 >15 -7$

implify the inequality to get $4d >8$ .
$4d >8$

Finally, divide both sides of the inequality by4 to solve for $d$ .
$\frac{4d}{4} > \frac{8}{4}$

implify the inequality to get $d >2$ .
$d >2$

Now let's solve the second inequality $-3d +4 \geq19$ for $d$ . We can start by subtracting4 from both sides of the inequality to isolate $-3d$ on the left side.
$-3d +4 -4 \geq19 -4$

implify the inequality to get $-3d \geq15$ .
$-3d \geq15$

Next, divide both sides of the inequality by -3 to solve for $d$ . Remember that when we divide or multiply an inequality by a negative number, we must reverse the direction of the inequality sign.
$\frac{-3d}{-3} \leq \frac{15}{-3}$

implify the inequality to get $d \leq -5$ .
$d \leq -5$

Now we have the solutions to the two inequalities $d >2$ and $d \leq -5$ . We can plot these on a number line. The number line should have an open circle at2 and a closed circle at -5. The line should extend to the right from2 and to the left from -5.