Solve the Inequality for x 2(4-2x)>1

$2 (4 - 2 x) > 1$

Divide each term in $2 (4 - 2 x) > 1$ by $2$ and simplify.

Divide each term in $2 (4 - 2 x) > 1$ by $2$ .

$\frac{2 (4 - 2 x)}{2} > \frac{1}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 (4 - 2 x)}{2} > \frac{1}{2}$

Divide $4 - 2 x$ by $1$ .

$4 - 2 x > \frac{1}{2}$

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

Subtract $4$ from both sides of the inequality.

$- 2 x > \frac{1}{2} - 4$

To write $- 4$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$- 2 x > \frac{1}{2} - 4 \cdot \frac{2}{2}$

Combine $- 4$ and $\frac{2}{2}$ .

$- 2 x > \frac{1}{2} + \frac{- 4 \cdot 2}{2}$

Combine the numerators over the common denominator.

$- 2 x > \frac{1 - 4 \cdot 2}{2}$

Simplify the numerator.

Multiply $- 4$ by $2$ .

$- 2 x > \frac{1 - 8}{2}$

Subtract $8$ from $1$ .

$- 2 x > \frac{- 7}{2}$

Move the negative in front of the fraction.

$- 2 x > - \frac{7}{2}$

Divide each term in $- 2 x > - \frac{7}{2}$ by $- 2$ and simplify.

Divide each term in $- 2 x > - \frac{7}{2}$ by $- 2$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- 2 x}{- 2} < \frac{- \frac{7}{2}}{- 2}$

Simplify the left side.

Cancel the common factor of $- 2$ .

Cancel the common factor.

$\frac{- 2 x}{- 2} < \frac{- \frac{7}{2}}{- 2}$

Divide $x$ by $1$ .

$x < \frac{- \frac{7}{2}}{- 2}$

Simplify the right side.

Multiply the numerator by the reciprocal of the denominator.

$x < - \frac{7}{2} \cdot \frac{1}{- 2}$

Move the negative in front of the fraction.

$x < - \frac{7}{2} (- \frac{1}{2})$

Multiply $- \frac{7}{2} (- \frac{1}{2})$ .

Multiply $- 1$ by $- 1$ .

$x < 1 (\frac{7}{2}) \frac{1}{2}$

Multiply $\frac{7}{2}$ by $1$ .

$x < \frac{7}{2} \cdot \frac{1}{2}$

Multiply $\frac{7}{2}$ by $\frac{1}{2}$ .

$x < \frac{7}{2 \cdot 2}$

Multiply $2$ by $2$ .

$x < \frac{7}{4}$

The result can be shown in multiple forms.

Inequality Form:

$x < \frac{7}{4}$

Interval Notation:

$(- \infty, \frac{7}{4})$

Solve the Inequality for x 2(4-2x)>1

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