Solve the Inequality for x 8-x>=5(8-x)

$8 - x \geq 5 (8 - x)$

Step 1

Simplify $5 (8 - x)$ .

Rewrite.

$8 - x \geq 0 + 0 + 5 (8 - x)$

Simplify by adding zeros.

$8 - x \geq 5 (8 - x)$

Apply the distributive property.

$8 - x \geq 5 \cdot 8 + 5 (- x)$

Multiply.

Multiply $5$ by $8$ .

$8 - x \geq 40 + 5 (- x)$

Multiply $- 1$ by $5$ .

$8 - x \geq 40 - 5 x$

Step 2

Move all terms containing $x$ to the left side of the inequality.

Add $5 x$ to both sides of the inequality.

$8 - x + 5 x \geq 40$

Add $- x$ and $5 x$ .

$8 + 4 x \geq 40$

Step 3

Move all terms not containing $x$ to the right side of the inequality.

Subtract $8$ from both sides of the inequality.

$4 x \geq 40 - 8$

Subtract $8$ from $40$ .

$4 x \geq 32$

Step 4

Divide each term in $4 x \geq 32$ by $4$ and simplify.

Divide each term in $4 x \geq 32$ by $4$ .

$\frac{4 x}{4} \geq \frac{32}{4}$

Simplify the left side.

Cancel the common factor of $4$ .

Cancel the common factor.

$\frac{4 x}{4} \geq \frac{32}{4}$

Divide $x$ by $1$ .

$x \geq \frac{32}{4}$

Simplify the right side.

Divide $32$ by $4$ .

$x \geq 8$

Step 5

The result can be shown in multiple forms.

Inequality Form:

$x \geq 8$

Interval Notation:

$[8, \infty)$