Solve the Inequality for x 3(x-4)>=5x+2

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

Simplify $3 (x - 4)$ .

Rewrite.

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

Simplify by adding zeros.

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

Apply the distributive property.

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

Multiply $3$ by $- 4$ .

$3 x - 12 \geq 5 x + 2$

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

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

$3 x - 12 - 5 x \geq 2$

Subtract $5 x$ from $3 x$ .

$- 2 x - 12 \geq 2$

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

Add $12$ to both sides of the inequality.

$- 2 x \geq 2 + 12$

Add $2$ and $12$ .

$- 2 x \geq 14$

Divide each term in $- 2 x \geq 14$ by $- 2$ and simplify.

Divide each term in $- 2 x \geq 14$ by $- 2$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- 2 x}{- 2} \leq \frac{14}{- 2}$

Simplify the left side.

Cancel the common factor of $- 2$ .

Cancel the common factor.

$\frac{- 2 x}{- 2} \leq \frac{14}{- 2}$

Divide $x$ by $1$ .

$x \leq \frac{14}{- 2}$

Simplify the right side.

Divide $14$ by $- 2$ .

$x \leq - 7$

The result can be shown in multiple forms.

Inequality Form:

$x \leq - 7$

Interval Notation:

$(- \infty, - 7]$

Solve the Inequality for x 3(x-4)>=5x+2

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