Solve for x -21<=7-4x<=24

$- 21 \leq 7 - 4 x \leq 24$

Step 1

Move all terms not containing $x$ from the center section of the inequality.

Subtract $7$ from each section of the inequality because it does not contain the variable we are trying to solve for.

$- 21 - 7 \leq - 4 x \leq 24 - 7$

Subtract $7$ from $- 21$ .

$- 28 \leq - 4 x \leq 24 - 7$

Subtract $7$ from $24$ .

$- 28 \leq - 4 x \leq 17$

Step 2

Divide each term in the inequality by $- 4$ .

$\frac{- 28}{- 4} \geq \frac{- 4 x}{- 4} \geq \frac{17}{- 4}$

Step 3

Divide $- 28$ by $- 4$ .

$7 \geq \frac{- 4 x}{- 4} \geq \frac{17}{- 4}$

Step 4

Cancel the common factor of $- 4$ .

Cancel the common factor.

$7 \geq \frac{- 4 x}{- 4} \geq \frac{17}{- 4}$

Divide $x$ by $1$ .

$7 \geq x \geq \frac{17}{- 4}$

Step 5

Move the negative in front of the fraction.

$7 \geq x \geq - \frac{17}{4}$

Step 6

Rewrite the interval so that the left value is less than the right value. This is the correct way to write an interval solution.

$- \frac{17}{4} \leq x \leq 7$

Step 7

The result can be shown in multiple forms.

Inequality Form:

$- \frac{17}{4} \leq x \leq 7$

Interval Notation:

$[- \frac{17}{4}, 7]$

Step 8