Solve the Inequality for x (x+15)/-3>-7

$\frac{x + 15}{- 3} > - 7$

Multiply both sides by $- 3$ .

$\frac{x + 15}{- 3} \cdot - 3 < - 7 \cdot - 3$

Simplify.

Simplify the left side.

Simplify $\frac{x + 15}{- 3} \cdot - 3$ .

Simplify terms.

Cancel the common factor of $3$ .

Factor $3$ out of $- 3$ .

$\frac{x + 15}{3 (- 1)} \cdot - 3 < - 7 \cdot - 3$

Factor $3$ out of $- 3$ .

$\frac{x + 15}{3 \cdot - 1} \cdot (3 \cdot - 1) < - 7 \cdot - 3$

Cancel the common factor.

$\frac{x + 15}{3 \cdot - 1} \cdot (3 \cdot - 1) < - 7 \cdot - 3$

Rewrite the expression.

$\frac{x + 15}{- 1} \cdot - 1 < - 7 \cdot - 3$

Combine $\frac{x + 15}{- 1}$ and $- 1$ .

$\frac{(x + 15) \cdot - 1}{- 1} < - 7 \cdot - 3$

Simplify the expression.

Move the negative one from the denominator of $\frac{(x + 15) \cdot - 1}{- 1}$ .

$- 1 \cdot ((x + 15) \cdot - 1) < - 7 \cdot - 3$

Rewrite $- 1 \cdot ((x + 15) \cdot - 1)$ as $- ((x + 15) \cdot - 1)$ .

$- ((x + 15) \cdot - 1) < - 7 \cdot - 3$

Apply the distributive property.

$- (x \cdot - 1 + 15 \cdot - 1) < - 7 \cdot - 3$

Simplify the expression.

Move $- 1$ to the left of $x$ .

$- (- 1 \cdot x + 15 \cdot - 1) < - 7 \cdot - 3$

Multiply $15$ by $- 1$ .

$- (- 1 \cdot x - 15) < - 7 \cdot - 3$

Rewrite $- 1 x$ as $- x$ .

$- (- x - 15) < - 7 \cdot - 3$

Apply the distributive property.

$- - x - - 15 < - 7 \cdot - 3$

Multiply $- - x$ .

Multiply $- 1$ by $- 1$ .

$1 x - - 15 < - 7 \cdot - 3$

Multiply $x$ by $1$ .

$x - - 15 < - 7 \cdot - 3$

Multiply $- 1$ by $- 15$ .

$x + 15 < - 7 \cdot - 3$

Simplify the right side.

Multiply $- 7$ by $- 3$ .

$x + 15 < 21$

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

Subtract $15$ from both sides of the inequality.

$x < 21 - 15$

Subtract $15$ from $21$ .

$x < 6$

The result can be shown in multiple forms.

Inequality Form:

$x < 6$

Interval Notation:

$(- \infty, 6)$

Solve the Inequality for x (x+15)/-3>-7

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