Solve for x 8(1/2x-1/4)>12-2x

$8 (\frac{1}{2} x - \frac{1}{4}) > 12 - 2 x$

Step 1

Simplify $8 (\frac{1}{2} x - \frac{1}{4})$ .

Rewrite.

$0 + 0 + 8 (\frac{1}{2} x - \frac{1}{4}) > 12 - 2 x$

Simplify by adding zeros.

$8 (\frac{1}{2} x - \frac{1}{4}) > 12 - 2 x$

Combine $\frac{1}{2}$ and $x$ .

$8 (\frac{x}{2} - \frac{1}{4}) > 12 - 2 x$

Apply the distributive property.

$8 \frac{x}{2} + 8 (- \frac{1}{4}) > 12 - 2 x$

Cancel the common factor of $2$ .

Factor $2$ out of $8$ .

$2 (4) \frac{x}{2} + 8 (- \frac{1}{4}) > 12 - 2 x$

Cancel the common factor.

$2 \cdot 4 \frac{x}{2} + 8 (- \frac{1}{4}) > 12 - 2 x$

Rewrite the expression.

$4 x + 8 (- \frac{1}{4}) > 12 - 2 x$

Cancel the common factor of $4$ .

Move the leading negative in $- \frac{1}{4}$ into the numerator.

$4 x + 8 (\frac{- 1}{4}) > 12 - 2 x$

Factor $4$ out of $8$ .

$4 x + 4 (2) \frac{- 1}{4} > 12 - 2 x$

Cancel the common factor.

$4 x + 4 \cdot 2 \frac{- 1}{4} > 12 - 2 x$

Rewrite the expression.

$4 x + 2 \cdot - 1 > 12 - 2 x$

Multiply $2$ by $- 1$ .

$4 x - 2 > 12 - 2 x$

Step 2

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

Add $2 x$ to both sides of the inequality.

$4 x - 2 + 2 x > 12$

Add $4 x$ and $2 x$ .

$6 x - 2 > 12$

Step 3

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

Add $2$ to both sides of the inequality.

$6 x > 12 + 2$

Add $12$ and $2$ .

$6 x > 14$

Step 4

Divide each term in $6 x > 14$ by $6$ and simplify.

Divide each term in $6 x > 14$ by $6$ .

$\frac{6 x}{6} > \frac{14}{6}$

Simplify the left side.

Cancel the common factor of $6$ .

Cancel the common factor.

$\frac{6 x}{6} > \frac{14}{6}$

Divide $x$ by $1$ .

$x > \frac{14}{6}$

Simplify the right side.

Cancel the common factor of $14$ and $6$ .

Factor $2$ out of $14$ .

$x > \frac{2 (7)}{6}$

Cancel the common factors.

Factor $2$ out of $6$ .

$x > \frac{2 \cdot 7}{2 \cdot 3}$

Cancel the common factor.

$x > \frac{2 \cdot 7}{2 \cdot 3}$

Rewrite the expression.

$x > \frac{7}{3}$

Step 5

The result can be shown in multiple forms.

Inequality Form:

$x > \frac{7}{3}$

Interval Notation:

$(\frac{7}{3}, \infty)$

Solve for x 8(1/2x-1/4)>12-2x

Related Questions

Support LCMGCF.com by disabling your adblocker.