Convert to Interval Notation 5x-7(x+1)>-9

$5 x - 7 (x + 1) > - 9$

Step 1

Simplify $5 x - 7 (x + 1)$ .

Simplify each term.

Apply the distributive property.

$5 x - 7 x - 7 \cdot 1 > - 9$

Multiply $- 7$ by $1$ .

$5 x - 7 x - 7 > - 9$

Subtract $7 x$ from $5 x$ .

$- 2 x - 7 > - 9$

Step 2

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

Add $7$ to both sides of the inequality.

$- 2 x > - 9 + 7$

Add $- 9$ and $7$ .

$- 2 x > - 2$

Step 3

Divide each term in $- 2 x > - 2$ by $- 2$ and simplify.

Divide each term in $- 2 x > - 2$ by $- 2$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- 2 x}{- 2} < \frac{- 2}{- 2}$

Simplify the left side.

Cancel the common factor of $- 2$ .

Cancel the common factor.

$\frac{- 2 x}{- 2} < \frac{- 2}{- 2}$

Divide $x$ by $1$ .

$x < \frac{- 2}{- 2}$

Simplify the right side.

Divide $- 2$ by $- 2$ .

$x < 1$

Step 4

Convert the inequality to interval notation.

$(- \infty, 1)$

Step 5

Convert to Interval Notation 5x-7(x+1)>-9

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