Solve the Inequality for x -2x<=(-3(x+1))/2

$- 2 x \leq \frac{- 3 (x + 1)}{2}$

Step 1

Multiply both sides by $2$ .

$- 2 x \cdot 2 \leq \frac{- 3 (x + 1)}{2} \cdot 2$

Step 2

Simplify.

Simplify the left side.

Multiply $2$ by $- 2$ .

$- 4 x \leq \frac{- 3 (x + 1)}{2} \cdot 2$

Simplify the right side.

Simplify $\frac{- 3 (x + 1)}{2} \cdot 2$ .

Cancel the common factor of $2$ .

Cancel the common factor.

$- 4 x \leq \frac{- 3 (x + 1)}{2} \cdot 2$

Rewrite the expression.

$- 4 x \leq - 3 (x + 1)$

Apply the distributive property.

$- 4 x \leq - 3 x - 3 \cdot 1$

Multiply $- 3$ by $1$ .

$- 4 x \leq - 3 x - 3$

Step 3

Solve for $x$ .

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

Add $3 x$ to both sides of the inequality.

$- 4 x + 3 x \leq - 3$

Add $- 4 x$ and $3 x$ .

$- x \leq - 3$

Divide each term in $- x \leq - 3$ by $- 1$ and simplify.

Divide each term in $- x \leq - 3$ by $- 1$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- x}{- 1} \geq \frac{- 3}{- 1}$

Simplify the left side.

Dividing two negative values results in a positive value.

$\frac{x}{1} \geq \frac{- 3}{- 1}$

Divide $x$ by $1$ .

$x \geq \frac{- 3}{- 1}$

Simplify the right side.

Divide $- 3$ by $- 1$ .

$x \geq 3$

Step 4

The result can be shown in multiple forms.

Inequality Form:

$x \geq 3$

Interval Notation:

$[3, \infty)$

Solve the Inequality for x -2x<=(-3(x+1))/2

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