Solve for x x+1>-5(7-2x)

$x + 1 > - 5 (7 - 2 x)$

Step 1

Simplify $- 5 (7 - 2 x)$ .

Rewrite.

$x + 1 > 0 + 0 - 5 (7 - 2 x)$

Simplify by adding zeros.

$x + 1 > - 5 (7 - 2 x)$

Apply the distributive property.

$x + 1 > - 5 \cdot 7 - 5 (- 2 x)$

Multiply.

Multiply $- 5$ by $7$ .

$x + 1 > - 35 - 5 (- 2 x)$

Multiply $- 2$ by $- 5$ .

$x + 1 > - 35 + 10 x$

Step 2

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

Subtract $10 x$ from both sides of the inequality.

$x + 1 - 10 x > - 35$

Subtract $10 x$ from $x$ .

$- 9 x + 1 > - 35$

Step 3

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

Subtract $1$ from both sides of the inequality.

$- 9 x > - 35 - 1$

Subtract $1$ from $- 35$ .

$- 9 x > - 36$

Step 4

Divide each term in $- 9 x > - 36$ by $- 9$ and simplify.

Divide each term in $- 9 x > - 36$ by $- 9$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- 9 x}{- 9} < \frac{- 36}{- 9}$

Simplify the left side.

Cancel the common factor of $- 9$ .

Cancel the common factor.

$\frac{- 9 x}{- 9} < \frac{- 36}{- 9}$

Divide $x$ by $1$ .

$x < \frac{- 36}{- 9}$

Simplify the right side.

Divide $- 36$ by $- 9$ .

$x < 4$

Step 5

The result can be shown in multiple forms.

Inequality Form:

$x < 4$

Interval Notation:

$(- \infty, 4)$

Solve for x x+1>-5(7-2x)

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