Solve for x -2(8x-4)<2x+5

$- 2 (8 x - 4) < 2 x + 5$

Step 1

Simplify $- 2 (8 x - 4)$ .

Rewrite.

$0 + 0 - 2 (8 x - 4) < 2 x + 5$

Simplify by adding zeros.

$- 2 (8 x - 4) < 2 x + 5$

Apply the distributive property.

$- 2 (8 x) - 2 \cdot - 4 < 2 x + 5$

Multiply.

Multiply $8$ by $- 2$ .

$- 16 x - 2 \cdot - 4 < 2 x + 5$

Multiply $- 2$ by $- 4$ .

$- 16 x + 8 < 2 x + 5$

Step 2

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

Subtract $2 x$ from both sides of the inequality.

$- 16 x + 8 - 2 x < 5$

Subtract $2 x$ from $- 16 x$ .

$- 18 x + 8 < 5$

Step 3

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

Subtract $8$ from both sides of the inequality.

$- 18 x < 5 - 8$

Subtract $8$ from $5$ .

$- 18 x < - 3$

Step 4

Divide each term in $- 18 x < - 3$ by $- 18$ and simplify.

Divide each term in $- 18 x < - 3$ by $- 18$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- 18 x}{- 18} > \frac{- 3}{- 18}$

Simplify the left side.

Cancel the common factor of $- 18$ .

Cancel the common factor.

$\frac{- 18 x}{- 18} > \frac{- 3}{- 18}$

Divide $x$ by $1$ .

$x > \frac{- 3}{- 18}$

Simplify the right side.

Cancel the common factor of $- 3$ and $- 18$ .

Factor $- 3$ out of $- 3$ .

$x > \frac{- 3 (1)}{- 18}$

Cancel the common factors.

Factor $- 3$ out of $- 18$ .

$x > \frac{- 3 \cdot 1}{- 3 \cdot 6}$

Cancel the common factor.

$x > \frac{- 3 \cdot 1}{- 3 \cdot 6}$

Rewrite the expression.

$x > \frac{1}{6}$

Step 5

The result can be shown in multiple forms.

Inequality Form:

$x > \frac{1}{6}$

Interval Notation:

$(\frac{1}{6}, \infty)$

Solve for x -2(8x-4)<2x+5

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