Solve for x 3x+2<=5(x-4)

$3 x + 2 \leq 5 (x - 4)$

Simplify $5 (x - 4)$ .

Rewrite.

$3 x + 2 \leq 0 + 0 + 5 (x - 4)$

Simplify by adding zeros.

$3 x + 2 \leq 5 (x - 4)$

Apply the distributive property.

$3 x + 2 \leq 5 x + 5 \cdot - 4$

Multiply $5$ by $- 4$ .

$3 x + 2 \leq 5 x - 20$

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

Subtract $5 x$ from both sides of the inequality.

$3 x + 2 - 5 x \leq - 20$

Subtract $5 x$ from $3 x$ .

$- 2 x + 2 \leq - 20$

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

Subtract $2$ from both sides of the inequality.

$- 2 x \leq - 20 - 2$

Subtract $2$ from $- 20$ .

$- 2 x \leq - 22$

Divide each term in $- 2 x \leq - 22$ by $- 2$ and simplify.

Divide each term in $- 2 x \leq - 22$ by $- 2$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- 2 x}{- 2} \geq \frac{- 22}{- 2}$

Simplify the left side.

Cancel the common factor of $- 2$ .

Cancel the common factor.

$\frac{- 2 x}{- 2} \geq \frac{- 22}{- 2}$

Divide $x$ by $1$ .

$x \geq \frac{- 22}{- 2}$

Simplify the right side.

Divide $- 22$ by $- 2$ .

$x \geq 11$

The result can be shown in multiple forms.

Inequality Form:

$x \geq 11$

Interval Notation:

$[11, \infty)$

Solve for x 3x+2<=5(x-4)

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