Solve the Inequality for x 2-10x>5-4(3-2x)

$2 - 10 x > 5 - 4 (3 - 2 x)$

Step 1

Simplify $5 - 4 (3 - 2 x)$ .

Simplify each term.

Apply the distributive property.

$2 - 10 x > 5 - 4 \cdot 3 - 4 (- 2 x)$

Multiply $- 4$ by $3$ .

$2 - 10 x > 5 - 12 - 4 (- 2 x)$

Multiply $- 2$ by $- 4$ .

$2 - 10 x > 5 - 12 + 8 x$

Subtract $12$ from $5$ .

$2 - 10 x > - 7 + 8 x$

Step 2

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

Subtract $8 x$ from both sides of the inequality.

$2 - 10 x - 8 x > - 7$

Subtract $8 x$ from $- 10 x$ .

$2 - 18 x > - 7$

Step 3

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

Subtract $2$ from both sides of the inequality.

$- 18 x > - 7 - 2$

Subtract $2$ from $- 7$ .

$- 18 x > - 9$

Step 4

Divide each term in $- 18 x > - 9$ by $- 18$ and simplify.

Divide each term in $- 18 x > - 9$ by $- 18$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- 18 x}{- 18} < \frac{- 9}{- 18}$

Simplify the left side.

Cancel the common factor of $- 18$ .

Cancel the common factor.

$\frac{- 18 x}{- 18} < \frac{- 9}{- 18}$

Divide $x$ by $1$ .

$x < \frac{- 9}{- 18}$

Simplify the right side.

Cancel the common factor of $- 9$ and $- 18$ .

Factor $- 9$ out of $- 9$ .

$x < \frac{- 9 (1)}{- 18}$

Cancel the common factors.

Factor $- 9$ out of $- 18$ .

$x < \frac{- 9 \cdot 1}{- 9 \cdot 2}$

Cancel the common factor.

$x < \frac{- 9 \cdot 1}{- 9 \cdot 2}$

Rewrite the expression.

$x < \frac{1}{2}$

Step 5

The result can be shown in multiple forms.

Inequality Form:

$x < \frac{1}{2}$

Interval Notation:

$(- \infty, \frac{1}{2})$

Solve the Inequality for x 2-10x>5-4(3-2x)

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