Solve the Inequality for x -5(-4+4x)>38-2x

$- 5 (- 4 + 4 x) > 38 - 2 x$

Step 1

Simplify $- 5 (- 4 + 4 x)$ .

Rewrite.

$0 + 0 - 5 (- 4 + 4 x) > 38 - 2 x$

Simplify by adding zeros.

$- 5 (- 4 + 4 x) > 38 - 2 x$

Apply the distributive property.

$- 5 \cdot - 4 - 5 (4 x) > 38 - 2 x$

Multiply.

Multiply $- 5$ by $- 4$ .

$20 - 5 (4 x) > 38 - 2 x$

Multiply $4$ by $- 5$ .

$20 - 20 x > 38 - 2 x$

Step 2

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

Add $2 x$ to both sides of the inequality.

$20 - 20 x + 2 x > 38$

Add $- 20 x$ and $2 x$ .

$20 - 18 x > 38$

Step 3

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

Subtract $20$ from both sides of the inequality.

$- 18 x > 38 - 20$

Subtract $20$ from $38$ .

$- 18 x > 18$

Step 4

Divide each term in $- 18 x > 18$ by $- 18$ and simplify.

Divide each term in $- 18 x > 18$ by $- 18$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- 18 x}{- 18} < \frac{18}{- 18}$

Simplify the left side.

Cancel the common factor of $- 18$ .

Cancel the common factor.

$\frac{- 18 x}{- 18} < \frac{18}{- 18}$

Divide $x$ by $1$ .

$x < \frac{18}{- 18}$

Simplify the right side.

Divide $18$ by $- 18$ .

$x < - 1$

Step 5

The result can be shown in multiple forms.

Inequality Form:

$x < - 1$

Interval Notation:

$(- \infty, - 1)$

Solve the Inequality for x -5(-4+4x)>38-2x

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