Solve for x 3(x-4)<=8x+13

$3 (x - 4) \leq 8 x + 13$

Step 1

Simplify $3 (x - 4)$ .

Rewrite.

$0 + 0 + 3 (x - 4) \leq 8 x + 13$

Simplify by adding zeros.

$3 (x - 4) \leq 8 x + 13$

Apply the distributive property.

$3 x + 3 \cdot - 4 \leq 8 x + 13$

Multiply $3$ by $- 4$ .

$3 x - 12 \leq 8 x + 13$

Step 2

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

Subtract $8 x$ from both sides of the inequality.

$3 x - 12 - 8 x \leq 13$

Subtract $8 x$ from $3 x$ .

$- 5 x - 12 \leq 13$

Step 3

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

Add $12$ to both sides of the inequality.

$- 5 x \leq 13 + 12$

Add $13$ and $12$ .

$- 5 x \leq 25$

Step 4

Divide each term in $- 5 x \leq 25$ by $- 5$ and simplify.

Divide each term in $- 5 x \leq 25$ by $- 5$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- 5 x}{- 5} \geq \frac{25}{- 5}$

Simplify the left side.

Cancel the common factor of $- 5$ .

Cancel the common factor.

$\frac{- 5 x}{- 5} \geq \frac{25}{- 5}$

Divide $x$ by $1$ .

$x \geq \frac{25}{- 5}$

Simplify the right side.

Divide $25$ by $- 5$ .

$x \geq - 5$

Step 5

The result can be shown in multiple forms.

Inequality Form:

$x \geq - 5$

Interval Notation:

$[- 5, \infty)$

Solve for x 3(x-4)<=8x+13

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