Solve the Inequality for x 12(1/2x-1/3)>8-2x

$12 (\frac{1}{2} x - \frac{1}{3}) > 8 - 2 x$

Step 1

Simplify $12 (\frac{1}{2} x - \frac{1}{3})$ .

Rewrite.

$0 + 0 + 12 (\frac{1}{2} x - \frac{1}{3}) > 8 - 2 x$

Simplify by adding zeros.

$12 (\frac{1}{2} x - \frac{1}{3}) > 8 - 2 x$

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

$12 (\frac{x}{2} - \frac{1}{3}) > 8 - 2 x$

Apply the distributive property.

$12 \frac{x}{2} + 12 (- \frac{1}{3}) > 8 - 2 x$

Cancel the common factor of $2$ .

Factor $2$ out of $12$ .

$2 (6) \frac{x}{2} + 12 (- \frac{1}{3}) > 8 - 2 x$

Cancel the common factor.

$2 \cdot 6 \frac{x}{2} + 12 (- \frac{1}{3}) > 8 - 2 x$

Rewrite the expression.

$6 x + 12 (- \frac{1}{3}) > 8 - 2 x$

Cancel the common factor of $3$ .

Move the leading negative in $- \frac{1}{3}$ into the numerator.

$6 x + 12 (\frac{- 1}{3}) > 8 - 2 x$

Factor $3$ out of $12$ .

$6 x + 3 (4) \frac{- 1}{3} > 8 - 2 x$

Cancel the common factor.

$6 x + 3 \cdot 4 \frac{- 1}{3} > 8 - 2 x$

Rewrite the expression.

$6 x + 4 \cdot - 1 > 8 - 2 x$

Multiply $4$ by $- 1$ .

$6 x - 4 > 8 - 2 x$

Step 2

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

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

$6 x - 4 + 2 x > 8$

Add $6 x$ and $2 x$ .

$8 x - 4 > 8$

Step 3

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

Add $4$ to both sides of the inequality.

$8 x > 8 + 4$

Add $8$ and $4$ .

$8 x > 12$

Step 4

Divide each term in $8 x > 12$ by $8$ and simplify.

Divide each term in $8 x > 12$ by $8$ .

$\frac{8 x}{8} > \frac{12}{8}$

Simplify the left side.

Cancel the common factor of $8$ .

Cancel the common factor.

$\frac{8 x}{8} > \frac{12}{8}$

Divide $x$ by $1$ .

$x > \frac{12}{8}$

Simplify the right side.

Cancel the common factor of $12$ and $8$ .

Factor $4$ out of $12$ .

$x > \frac{4 (3)}{8}$

Cancel the common factors.

Factor $4$ out of $8$ .

$x > \frac{4 \cdot 3}{4 \cdot 2}$

Cancel the common factor.

$x > \frac{4 \cdot 3}{4 \cdot 2}$

Rewrite the expression.

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

Step 5

The result can be shown in multiple forms.

Inequality Form:

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

Interval Notation:

$(\frac{3}{2}, \infty)$

Solve the Inequality for x 12(1/2x-1/3)>8-2x

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