Solve the Inequality for x -34<-2(4x-1)

$- 34 < - 2 (4 x - 1)$

Rewrite so $x$ is on the left side of the inequality.

$- 2 (4 x - 1) > - 34$

Divide each term in $- 2 (4 x - 1) > - 34$ by $- 2$ and simplify.

Divide each term in $- 2 (4 x - 1) > - 34$ by $- 2$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- 2 (4 x - 1)}{- 2} < \frac{- 34}{- 2}$

Simplify the left side.

Cancel the common factor of $- 2$ .

Cancel the common factor.

$\frac{- 2 (4 x - 1)}{- 2} < \frac{- 34}{- 2}$

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

$4 x - 1 < \frac{- 34}{- 2}$

Simplify the right side.

Divide $- 34$ by $- 2$ .

$4 x - 1 < 17$

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

Add $1$ to both sides of the inequality.

$4 x < 17 + 1$

Add $17$ and $1$ .

$4 x < 18$

Divide each term in $4 x < 18$ by $4$ and simplify.

Divide each term in $4 x < 18$ by $4$ .

$\frac{4 x}{4} < \frac{18}{4}$

Simplify the left side.

Cancel the common factor of $4$ .

Cancel the common factor.

$\frac{4 x}{4} < \frac{18}{4}$

Divide $x$ by $1$ .

$x < \frac{18}{4}$

Simplify the right side.

Cancel the common factor of $18$ and $4$ .

Factor $2$ out of $18$ .

$x < \frac{2 (9)}{4}$

Cancel the common factors.

Factor $2$ out of $4$ .

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

Cancel the common factor.

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

Rewrite the expression.

$x < \frac{9}{2}$

The result can be shown in multiple forms.

Inequality Form:

$x < \frac{9}{2}$

Interval Notation:

$(- \infty, \frac{9}{2})$

Solve the Inequality for x -34<-2(4x-1)

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