Math

QuestionSolve the compound inequality: 175x624-17 \leq 5x - 6 \leq 24.

Studdy Solution

STEP 1

Assumptions1. The inequality is 175x624-17 \leq5x -6 \leq24 . We are solving for xx

STEP 2

The given inequality is a compound inequality. It can be split into two separate inequalities 175x6-17 \leq5x -6 and 5x6245x -6 \leq24. We will solve each inequality separately.

STEP 3

First, let's solve the inequality 175x6-17 \leq5x -6. To isolate xx, we need to get rid of the 6-6 on the right side of the inequality. We can do this by adding 66 to both sides of the inequality.
17+65x6+6-17 +6 \leq5x -6 +6

STEP 4

implify the inequality.
-11 \leqx

STEP 5

Now, to isolate xx, we divide both sides of the inequality by 55.
1155x5\frac{-11}{5} \leq \frac{5x}{5}

STEP 6

implify the inequality to get the solution for xx.
2.2x-2.2 \leq x

STEP 7

Now, let's solve the second inequality 5x6245x -6 \leq24. Again, we start by getting rid of the 6-6 on the right side of the inequality. We do this by adding 66 to both sides of the inequality.
5x6+624+65x -6 +6 \leq24 +6

STEP 8

implify the inequality.
5x305x \leq30

STEP 9

Now, to isolate xx, we divide both sides of the inequality by 55.
5x5305\frac{5x}{5} \leq \frac{30}{5}

STEP 10

implify the inequality to get the solution for xx.
x6x \leq6

STEP 11

Now that we have solved both inequalities, we can combine them to get the solution for the compound inequality..x6-. \leq x \leq6So, the solution to the inequality 175x624-17 \leq5x -6 \leq24 is .x6-. \leq x \leq6.

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