Solve the Inequality for x 3/2x-7>=-3(-3x-5)-7

$\frac{3}{2} x - 7 \geq - 3 (- 3 x - 5) - 7$

Combine $\frac{3}{2}$ and $x$ .

$\frac{3 x}{2} - 7 \geq - 3 (- 3 x - 5) - 7$

Simplify $- 3 (- 3 x - 5) - 7$ .

Simplify each term.

Apply the distributive property.

$\frac{3 x}{2} - 7 \geq - 3 (- 3 x) - 3 \cdot - 5 - 7$

Multiply $- 3$ by $- 3$ .

$\frac{3 x}{2} - 7 \geq 9 x - 3 \cdot - 5 - 7$

Multiply $- 3$ by $- 5$ .

$\frac{3 x}{2} - 7 \geq 9 x + 15 - 7$

Subtract $7$ from $15$ .

$\frac{3 x}{2} - 7 \geq 9 x + 8$

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

Subtract $9 x$ from both sides of the inequality.

$\frac{3 x}{2} - 7 - 9 x \geq 8$

To write $- 9 x$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{3 x}{2} - 9 x \cdot \frac{2}{2} - 7 \geq 8$

Combine $- 9 x$ and $\frac{2}{2}$ .

$\frac{3 x}{2} + \frac{- 9 x \cdot 2}{2} - 7 \geq 8$

Combine the numerators over the common denominator.

$\frac{3 x - 9 x \cdot 2}{2} - 7 \geq 8$

Simplify each term.

Simplify the numerator.

Factor $3 x$ out of $3 x - 9 x \cdot 2$ .

Factor $3 x$ out of $3 x$ .

$\frac{3 x (1) - 9 x \cdot 2}{2} - 7 \geq 8$

Factor $3 x$ out of $- 9 x \cdot 2$ .

$\frac{3 x (1) + 3 x (- 3 \cdot 2)}{2} - 7 \geq 8$

Factor $3 x$ out of $3 x (1) + 3 x (- 3 \cdot 2)$ .

$\frac{3 x (1 - 3 \cdot 2)}{2} - 7 \geq 8$

Multiply $- 3$ by $2$ .

$\frac{3 x (1 - 6)}{2} - 7 \geq 8$

Subtract $6$ from $1$ .

$\frac{3 x \cdot - 5}{2} - 7 \geq 8$

Multiply $- 5$ by $3$ .

$\frac{- 15 x}{2} - 7 \geq 8$

Move the negative in front of the fraction.

$- \frac{15 x}{2} - 7 \geq 8$

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

Add $7$ to both sides of the inequality.

$- \frac{15 x}{2} \geq 8 + 7$

Add $8$ and $7$ .

$- \frac{15 x}{2} \geq 15$

Divide each term in $- \frac{15 x}{2} \geq 15$ by $- 1$ and simplify.

Divide each term in $- \frac{15 x}{2} \geq 15$ by $- 1$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- \frac{15 x}{2}}{- 1} \leq \frac{15}{- 1}$

Simplify the left side.

Dividing two negative values results in a positive value.

$\frac{\frac{15 x}{2}}{1} \leq \frac{15}{- 1}$

Divide $\frac{15 x}{2}$ by $1$ .

$\frac{15 x}{2} \leq \frac{15}{- 1}$

Simplify the right side.

Divide $15$ by $- 1$ .

$\frac{15 x}{2} \leq - 15$

Multiply both sides by $2$ .

$\frac{15 x}{2} \cdot 2 \leq - 15 \cdot 2$

Simplify.

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{15 x}{2} \cdot 2 \leq - 15 \cdot 2$

Rewrite the expression.

$15 x \leq - 15 \cdot 2$

Simplify the right side.

Multiply $- 15$ by $2$ .

$15 x \leq - 30$

Divide each term in $15 x \leq - 30$ by $15$ and simplify.

Divide each term in $15 x \leq - 30$ by $15$ .

$\frac{15 x}{15} \leq \frac{- 30}{15}$

Simplify the left side.

Cancel the common factor of $15$ .

Cancel the common factor.

$\frac{15 x}{15} \leq \frac{- 30}{15}$

Divide $x$ by $1$ .

$x \leq \frac{- 30}{15}$

Simplify the right side.

Divide $- 30$ by $15$ .

$x \leq - 2$

The result can be shown in multiple forms.

Inequality Form:

$x \leq - 2$

Interval Notation:

$(- \infty, - 2]$

Solve the Inequality for x 3/2x-7>=-3(-3x-5)-7

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