Solve the Inequality for x (5-(9-4x))/-2<-5

$\frac{5 - (9 - 4 x)}{- 2} < - 5$

Step 1

Multiply both sides by $- 2$ .

$\frac{5 - (9 - 4 x)}{- 2} \cdot - 2 > - 5 \cdot - 2$

Step 2

Simplify.

Simplify the left side.

Simplify $\frac{5 - (9 - 4 x)}{- 2} \cdot - 2$ .

Simplify the numerator.

Apply the distributive property.

$\frac{5 - 1 \cdot 9 - (- 4 x)}{- 2} \cdot - 2 > - 5 \cdot - 2$

Multiply $- 1$ by $9$ .

$\frac{5 - 9 - (- 4 x)}{- 2} \cdot - 2 > - 5 \cdot - 2$

Multiply $- 4$ by $- 1$ .

$\frac{5 - 9 + 4 x}{- 2} \cdot - 2 > - 5 \cdot - 2$

Subtract $9$ from $5$ .

$\frac{- 4 + 4 x}{- 2} \cdot - 2 > - 5 \cdot - 2$

Factor $4$ out of $- 4 + 4 x$ .

Factor $4$ out of $- 4$ .

$\frac{4 \cdot - 1 + 4 x}{- 2} \cdot - 2 > - 5 \cdot - 2$

Factor $4$ out of $4 \cdot - 1 + 4 x$ .

$\frac{4 (- 1 + x)}{- 2} \cdot - 2 > - 5 \cdot - 2$

Simplify terms.

Cancel the common factor of $2$ .

Factor $2$ out of $- 2$ .

$\frac{4 (- 1 + x)}{2 (- 1)} \cdot - 2 > - 5 \cdot - 2$

Factor $2$ out of $- 2$ .

$\frac{4 (- 1 + x)}{2 \cdot - 1} \cdot (2 \cdot - 1) > - 5 \cdot - 2$

Cancel the common factor.

$\frac{4 (- 1 + x)}{2 \cdot - 1} \cdot (2 \cdot - 1) > - 5 \cdot - 2$

Rewrite the expression.

$\frac{4 (- 1 + x)}{- 1} \cdot - 1 > - 5 \cdot - 2$

Combine $\frac{4 (- 1 + x)}{- 1}$ and $- 1$ .

$\frac{4 (- 1 + x) \cdot - 1}{- 1} > - 5 \cdot - 2$

Simplify the expression.

Multiply $- 1$ by $4$ .

$\frac{- 4 (- 1 + x)}{- 1} > - 5 \cdot - 2$

Move the negative one from the denominator of $\frac{- 4 (- 1 + x)}{- 1}$ .

$- 1 \cdot (- 4 (- 1 + x)) > - 5 \cdot - 2$

Rewrite $- 1 \cdot (- 4 (- 1 + x))$ as $- (- 4 (- 1 + x))$ .

$- (- 4 (- 1 + x)) > - 5 \cdot - 2$

Apply the distributive property.

$- (- 4 \cdot - 1 - 4 x) > - 5 \cdot - 2$

Multiply $- 4$ by $- 1$ .

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

Apply the distributive property.

$- 1 \cdot 4 - (- 4 x) > - 5 \cdot - 2$

Simplify the expression.

Multiply $- 1$ by $4$ .

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

Multiply $- 4$ by $- 1$ .

$- 4 + 4 x > - 5 \cdot - 2$

Reorder $- 4$ and $4 x$ .

$4 x - 4 > - 5 \cdot - 2$

Simplify the right side.

Multiply $- 5$ by $- 2$ .

$4 x - 4 > 10$

Step 3

Solve for $x$ .

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

Add $4$ to both sides of the inequality.

$4 x > 10 + 4$

Add $10$ and $4$ .

$4 x > 14$

Divide each term in $4 x > 14$ by $4$ and simplify.

Divide each term in $4 x > 14$ by $4$ .

$\frac{4 x}{4} > \frac{14}{4}$

Simplify the left side.

Cancel the common factor of $4$ .

Cancel the common factor.

$\frac{4 x}{4} > \frac{14}{4}$

Divide $x$ by $1$ .

$x > \frac{14}{4}$

Simplify the right side.

Cancel the common factor of $14$ and $4$ .

Factor $2$ out of $14$ .

$x > \frac{2 (7)}{4}$

Cancel the common factors.

Factor $2$ out of $4$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Step 4

The result can be shown in multiple forms.

Inequality Form:

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

Interval Notation:

$(\frac{7}{2}, \infty)$

Solve the Inequality for x (5-(9-4x))/-2<-5

Related Questions

Support LCMGCF.com by disabling your adblocker.