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

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

Simplify $3 (x - 2)$ .

Rewrite.

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

Simplify by adding zeros.

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

Apply the distributive property.

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

Multiply $3$ by $- 2$ .

$2 x + 5 \leq 3 x - 6$

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

Subtract $3 x$ from both sides of the inequality.

$2 x + 5 - 3 x \leq - 6$

Subtract $3 x$ from $2 x$ .

$- x + 5 \leq - 6$

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

Subtract $5$ from both sides of the inequality.

$- x \leq - 6 - 5$

Subtract $5$ from $- 6$ .

$- x \leq - 11$

Divide each term in $- x \leq - 11$ by $- 1$ and simplify.

Divide each term in $- x \leq - 11$ by $- 1$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- x}{- 1} \geq \frac{- 11}{- 1}$

Simplify the left side.

Dividing two negative values results in a positive value.

$\frac{x}{1} \geq \frac{- 11}{- 1}$

Divide $x$ by $1$ .

$x \geq \frac{- 11}{- 1}$

Simplify the right side.

Divide $- 11$ by $- 1$ .

$x \geq 11$

The result can be shown in multiple forms.

Inequality Form:

$x \geq 11$

Interval Notation:

$[11, \infty)$

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

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