Solve the Inequality for x 7-1/8(6x-4)<8

$7 - \frac{1}{8} (6 x - 4) < 8$

Simplify $7 - \frac{1}{8} \cdot (6 x - 4)$ .

Simplify each term.

Apply the distributive property.

$7 - \frac{1}{8} (6 x) - \frac{1}{8} \cdot - 4 < 8$

Cancel the common factor of $2$ .

Move the leading negative in $- \frac{1}{8}$ into the numerator.

$7 + \frac{- 1}{8} (6 x) - \frac{1}{8} \cdot - 4 < 8$

Factor $2$ out of $8$ .

$7 + \frac{- 1}{2 (4)} (6 x) - \frac{1}{8} \cdot - 4 < 8$

Factor $2$ out of $6 x$ .

$7 + \frac{- 1}{2 (4)} (2 (3 x)) - \frac{1}{8} \cdot - 4 < 8$

Cancel the common factor.

$7 + \frac{- 1}{2 \cdot 4} (2 (3 x)) - \frac{1}{8} \cdot - 4 < 8$

Rewrite the expression.

$7 + \frac{- 1}{4} (3 x) - \frac{1}{8} \cdot - 4 < 8$

Combine $3$ and $\frac{- 1}{4}$ .

$7 + \frac{3 \cdot - 1}{4} x - \frac{1}{8} \cdot - 4 < 8$

Multiply $3$ by $- 1$ .

$7 + \frac{- 3}{4} x - \frac{1}{8} \cdot - 4 < 8$

Combine $\frac{- 3}{4}$ and $x$ .

$7 + \frac{- 3 x}{4} - \frac{1}{8} \cdot - 4 < 8$

Cancel the common factor of $4$ .

Move the leading negative in $- \frac{1}{8}$ into the numerator.

$7 + \frac{- 3 x}{4} + \frac{- 1}{8} \cdot - 4 < 8$

Factor $4$ out of $8$ .

$7 + \frac{- 3 x}{4} + \frac{- 1}{4 (2)} \cdot - 4 < 8$

Factor $4$ out of $- 4$ .

$7 + \frac{- 3 x}{4} + \frac{- 1}{4 \cdot 2} \cdot (4 \cdot - 1) < 8$

Cancel the common factor.

$7 + \frac{- 3 x}{4} + \frac{- 1}{4 \cdot 2} \cdot (4 \cdot - 1) < 8$

Rewrite the expression.

$7 + \frac{- 3 x}{4} + \frac{- 1}{2} \cdot - 1 < 8$

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

$7 + \frac{- 3 x}{4} + \frac{- - 1}{2} < 8$

Multiply $- 1$ by $- 1$ .

$7 + \frac{- 3 x}{4} + \frac{1}{2} < 8$

Move the negative in front of the fraction.

$7 - \frac{3 x}{4} + \frac{1}{2} < 8$

To write $7$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$- \frac{3 x}{4} + 7 \cdot \frac{2}{2} + \frac{1}{2} < 8$

Combine $7$ and $\frac{2}{2}$ .

$- \frac{3 x}{4} + \frac{7 \cdot 2}{2} + \frac{1}{2} < 8$

Combine the numerators over the common denominator.

$- \frac{3 x}{4} + \frac{7 \cdot 2 + 1}{2} < 8$

Simplify the numerator.

Multiply $7$ by $2$ .

$- \frac{3 x}{4} + \frac{14 + 1}{2} < 8$

Add $14$ and $1$ .

$- \frac{3 x}{4} + \frac{15}{2} < 8$

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

Subtract $\frac{15}{2}$ from both sides of the inequality.

$- \frac{3 x}{4} < 8 - \frac{15}{2}$

To write $8$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$- \frac{3 x}{4} < 8 \cdot \frac{2}{2} - \frac{15}{2}$

Combine $8$ and $\frac{2}{2}$ .

$- \frac{3 x}{4} < \frac{8 \cdot 2}{2} - \frac{15}{2}$

Combine the numerators over the common denominator.

$- \frac{3 x}{4} < \frac{8 \cdot 2 - 15}{2}$

Simplify the numerator.

Multiply $8$ by $2$ .

$- \frac{3 x}{4} < \frac{16 - 15}{2}$

Subtract $15$ from $16$ .

$- \frac{3 x}{4} < \frac{1}{2}$

Divide each term in $- \frac{3 x}{4} < \frac{1}{2}$ by $- 1$ and simplify.

Divide each term in $- \frac{3 x}{4} < \frac{1}{2}$ by $- 1$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- \frac{3 x}{4}}{- 1} > \frac{\frac{1}{2}}{- 1}$

Simplify the left side.

Dividing two negative values results in a positive value.

$\frac{\frac{3 x}{4}}{1} > \frac{\frac{1}{2}}{- 1}$

Divide $\frac{3 x}{4}$ by $1$ .

$\frac{3 x}{4} > \frac{\frac{1}{2}}{- 1}$

Simplify the right side.

Move the negative one from the denominator of $\frac{\frac{1}{2}}{- 1}$ .

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

Rewrite $- 1 \cdot \frac{1}{2}$ as $- \frac{1}{2}$ .

$\frac{3 x}{4} > - \frac{1}{2}$

Multiply both sides by $4$ .

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

Simplify.

Simplify the left side.

Cancel the common factor of $4$ .

Cancel the common factor.

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

Rewrite the expression.

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

Simplify the right side.

Simplify $- \frac{1}{2} \cdot 4$ .

Cancel the common factor of $2$ .

Move the leading negative in $- \frac{1}{2}$ into the numerator.

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

Factor $2$ out of $4$ .

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

Cancel the common factor.

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

Rewrite the expression.

$3 x > - 1 \cdot 2$

Multiply $- 1$ by $2$ .

$3 x > - 2$

Divide each term in $3 x > - 2$ by $3$ and simplify.

Divide each term in $3 x > - 2$ by $3$ .

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

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

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

Divide $x$ by $1$ .

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

Simplify the right side.

Move the negative in front of the fraction.

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

The result can be shown in multiple forms.

Inequality Form:

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

Interval Notation:

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

Solve the Inequality for x 7-1/8(6x-4)<8

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