Solved on Sep 28, 2023

Find the values of $x$ that satisfy the inequality $\frac{x+2}{x-5} > \frac{3}{5}$ .

STEP 1

Assumptions1. The ratio of $(x+)$ to $(x-5)$ is greater than $\frac{3}{5}$ . . We need to solve for $x$ .

STEP 2

First, we need to set up the inequality. The problem states that the ratio of $(x+2)$ to $(x-5)$ is greater than $\frac{}{5}$ , so we can write this as $(x+2)/(x-5) >/5$

STEP 3

To solve for $x$ , we can cross-multiply to get rid of the fractions. This gives us $5(x+2) >3(x-5)$

STEP 4

Expand both sides of the inequality $x +10 >3x -15$

STEP 5

Now, we can subtract $3x$ from both sides to isolate $x$ on one side of the inequality $5x -3x > -15 -10$

STEP 6

implify the inequality $2x > -25$

STEP 7

Finally, divide both sides by2 to solve for $x$ $x > -25/2$ So, $x$ must be greater than $-25/2$ or $-12.5$ .

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Find the values of $x$ that satisfy the inequality $\frac{x+2}{x-5} > \frac{3}{5}$ .

STEP 1

Assumptions1. The ratio of $(x+)$ to $(x-5)$ is greater than $\frac{3}{5}$ . . We need to solve for $x$ .

STEP 2

First, we need to set up the inequality. The problem states that the ratio of $(x+2)$ to $(x-5)$ is greater than $\frac{}{5}$ , so we can write this as $(x+2)/(x-5) >/5$

STEP 3

To solve for $x$ , we can cross-multiply to get rid of the fractions. This gives us $5(x+2) >3(x-5)$

STEP 4

Expand both sides of the inequality $x +10 >3x -15$

STEP 5

Now, we can subtract $3x$ from both sides to isolate $x$ on one side of the inequality $5x -3x > -15 -10$

STEP 6

implify the inequality $2x > -25$

STEP 7

Finally, divide both sides by2 to solve for $x$ $x > -25/2$ So, $x$ must be greater than $-25/2$ or $-12.5$ .

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Find the values of xxx that satisfy the inequality x+2x−5>35\frac{x+2}{x-5} > \frac{3}{5}x−5x+2​>53​.

STEP 1

Assumptions1. The ratio of (x+)(x+)(x+) to (x−5)(x-5)(x−5) is greater than 35\frac{3}{5}53​. . We need to solve for xxx.

STEP 2

First, we need to set up the inequality. The problem states that the ratio of (x+2)(x+2)(x+2) to (x−5)(x-5)(x−5) is greater than 5\frac{}{5}5​, so we can write this as(x+2)/(x−5)>/5(x+2)/(x-5) >/5(x+2)/(x−5)>/5

STEP 3

To solve for xxx, we can cross-multiply to get rid of the fractions. This gives us5(x+2)>3(x−5)5(x+2) >3(x-5)5(x+2)>3(x−5)

STEP 4

Expand both sides of the inequalityx+10>3x−15x +10 >3x -15x+10>3x−15

STEP 5

Now, we can subtract 3x3x3x from both sides to isolate xxx on one side of the inequality5x−3x>−15−105x -3x > -15 -105x−3x>−15−10

STEP 6

implify the inequality2x>−252x > -252x>−25

STEP 7

Finally, divide both sides by2 to solve for xxxx>−25/2x > -25/2x>−25/2So, xxx must be greater than −25/2-25/2−25/2 or −12.5-12.5−12.5.

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

Find the values of $x$ that satisfy the inequality $\frac{x+2}{x-5} > \frac{3}{5}$ .

Assumptions1. The ratio of $(x+)$ to $(x-5)$ is greater than $\frac{3}{5}$ . . We need to solve for $x$ .

First, we need to set up the inequality. The problem states that the ratio of $(x+2)$ to $(x-5)$ is greater than $\frac{}{5}$ , so we can write this as $(x+2)/(x-5) >/5$

To solve for $x$ , we can cross-multiply to get rid of the fractions. This gives us $5(x+2) >3(x-5)$

Expand both sides of the inequality $x +10 >3x -15$

Now, we can subtract $3x$ from both sides to isolate $x$ on one side of the inequality $5x -3x > -15 -10$

implify the inequality $2x > -25$

Finally, divide both sides by2 to solve for $x$ $x > -25/2$ So, $x$ must be greater than $-25/2$ or $-12.5$ .