Math

Question Find the values of xx that satisfy the inequality x+2x5>35\frac{x+2}{x-5} > \frac{3}{5}.

Studdy Solution

STEP 1

Assumptions1. The ratio of (x+)(x+) to (x5)(x-5) is greater than 35\frac{3}{5}. . We need to solve for xx.

STEP 2

First, we need to set up the inequality. The problem states that the ratio of (x+2)(x+2) to (x5)(x-5) is greater than 5\frac{}{5}, so we can write this as(x+2)/(x5)>/5(x+2)/(x-5) >/5

STEP 3

To solve for xx, we can cross-multiply to get rid of the fractions. This gives us5(x+2)>3(x5)5(x+2) >3(x-5)

STEP 4

Expand both sides of the inequalityx+10>3x15x +10 >3x -15

STEP 5

Now, we can subtract 3x3x from both sides to isolate xx on one side of the inequality5x3x>15105x -3x > -15 -10

STEP 6

implify the inequality2x>252x > -25

STEP 7

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

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