Solve the Inequality for x -8(x-4)-3<=5

$- 8 (x - 4) - 3 \leq 5$

Step 1

Simplify $- 8 (x - 4) - 3$ .

Simplify each term.

Apply the distributive property.

$- 8 x - 8 \cdot - 4 - 3 \leq 5$

Multiply $- 8$ by $- 4$ .

$- 8 x + 32 - 3 \leq 5$

Subtract $3$ from $32$ .

$- 8 x + 29 \leq 5$

Step 2

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

Subtract $29$ from both sides of the inequality.

$- 8 x \leq 5 - 29$

Subtract $29$ from $5$ .

$- 8 x \leq - 24$

Step 3

Divide each term in $- 8 x \leq - 24$ by $- 8$ and simplify.

Divide each term in $- 8 x \leq - 24$ by $- 8$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- 8 x}{- 8} \geq \frac{- 24}{- 8}$

Simplify the left side.

Cancel the common factor of $- 8$ .

Cancel the common factor.

$\frac{- 8 x}{- 8} \geq \frac{- 24}{- 8}$

Divide $x$ by $1$ .

$x \geq \frac{- 24}{- 8}$

Simplify the right side.

Divide $- 24$ by $- 8$ .

$x \geq 3$

Step 4

The result can be shown in multiple forms.

Inequality Form:

$x \geq 3$

Interval Notation:

$[3, \infty)$

Solve the Inequality for x -8(x-4)-3<=5

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