Convert to Set Notation -3(x+2)<=5x+7

$- 3 (x + 2) \leq 5 x + 7$

Step 1

Solve $x \geq - \frac{13}{8}$ .

Simplify $- 3 (x + 2)$ .

Rewrite.

$0 + 0 - 3 (x + 2) \leq 5 x + 7$

Simplify by adding zeros.

$- 3 (x + 2) \leq 5 x + 7$

Apply the distributive property.

$- 3 x - 3 \cdot 2 \leq 5 x + 7$

Multiply $- 3$ by $2$ .

$- 3 x - 6 \leq 5 x + 7$

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

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

$- 3 x - 6 - 5 x \leq 7$

Subtract $5 x$ from $- 3 x$ .

$- 8 x - 6 \leq 7$

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

Add $6$ to both sides of the inequality.

$- 8 x \leq 7 + 6$

Add $7$ and $6$ .

$- 8 x \leq 13$

Divide each term in $- 8 x \leq 13$ by $- 8$ and simplify.

Divide each term in $- 8 x \leq 13$ by $- 8$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- 8 x}{- 8} \geq \frac{13}{- 8}$

Simplify the left side.

Cancel the common factor of $- 8$ .

Cancel the common factor.

$\frac{- 8 x}{- 8} \geq \frac{13}{- 8}$

Divide $x$ by $1$ .

$x \geq \frac{13}{- 8}$

Simplify the right side.

Move the negative in front of the fraction.

$x \geq - \frac{13}{8}$

Step 2

Use the inequality $x \geq - \frac{13}{8}$ to build the set notation.

${x | x \geq - \frac{13}{8}}$

Step 3

Convert to Set Notation -3(x+2)<=5x+7

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