Solve the Inequality for x 3x-7(x+3)<-13

$3 x - 7 (x + 3) < - 13$

Step 1

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

Simplify each term.

Apply the distributive property.

$3 x - 7 x - 7 \cdot 3 < - 13$

Multiply $- 7$ by $3$ .

$3 x - 7 x - 21 < - 13$

Subtract $7 x$ from $3 x$ .

$- 4 x - 21 < - 13$

Step 2

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

Add $21$ to both sides of the inequality.

$- 4 x < - 13 + 21$

Add $- 13$ and $21$ .

$- 4 x < 8$

Step 3

Divide each term in $- 4 x < 8$ by $- 4$ and simplify.

Divide each term in $- 4 x < 8$ by $- 4$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- 4 x}{- 4} > \frac{8}{- 4}$

Simplify the left side.

Cancel the common factor of $- 4$ .

Cancel the common factor.

$\frac{- 4 x}{- 4} > \frac{8}{- 4}$

Divide $x$ by $1$ .

$x > \frac{8}{- 4}$

Simplify the right side.

Divide $8$ by $- 4$ .

$x > - 2$

Step 4

The result can be shown in multiple forms.

Inequality Form:

$x > - 2$

Interval Notation:

$(- 2, \infty)$

Solve the Inequality for x 3x-7(x+3)<-13

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