Solve for x 9x-1<3/4*(16x-2)

$9 x - 1 < \frac{3}{4} \cdot (16 x - 2)$

Step 1

Simplify $\frac{3}{4} \cdot (16 x - 2)$ .

Rewrite.

$9 x - 1 < 0 + 0 + \frac{3}{4} \cdot (16 x - 2)$

Simplify by adding zeros.

$9 x - 1 < \frac{3}{4} \cdot (16 x - 2)$

Apply the distributive property.

$9 x - 1 < \frac{3}{4} (16 x) + \frac{3}{4} \cdot - 2$

Cancel the common factor of $4$ .

Factor $4$ out of $16 x$ .

$9 x - 1 < \frac{3}{4} (4 (4 x)) + \frac{3}{4} \cdot - 2$

Cancel the common factor.

$9 x - 1 < \frac{3}{4} (4 (4 x)) + \frac{3}{4} \cdot - 2$

Rewrite the expression.

$9 x - 1 < 3 (4 x) + \frac{3}{4} \cdot - 2$

Multiply $4$ by $3$ .

$9 x - 1 < 12 x + \frac{3}{4} \cdot - 2$

Cancel the common factor of $2$ .

Factor $2$ out of $4$ .

$9 x - 1 < 12 x + \frac{3}{2 (2)} \cdot - 2$

Factor $2$ out of $- 2$ .

$9 x - 1 < 12 x + \frac{3}{2 \cdot 2} \cdot (2 \cdot - 1)$

Cancel the common factor.

$9 x - 1 < 12 x + \frac{3}{2 \cdot 2} \cdot (2 \cdot - 1)$

Rewrite the expression.

$9 x - 1 < 12 x + \frac{3}{2} \cdot - 1$

Combine $\frac{3}{2}$ and $- 1$ .

$9 x - 1 < 12 x + \frac{3 \cdot - 1}{2}$

Simplify the expression.

Multiply $3$ by $- 1$ .

$9 x - 1 < 12 x + \frac{- 3}{2}$

Move the negative in front of the fraction.

$9 x - 1 < 12 x - \frac{3}{2}$

Step 2

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

Subtract $12 x$ from both sides of the inequality.

$9 x - 1 - 12 x < - \frac{3}{2}$

Subtract $12 x$ from $9 x$ .

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

Step 3

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

Add $1$ to both sides of the inequality.

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

Write $1$ as a fraction with a common denominator.

$- 3 x < - \frac{3}{2} + \frac{2}{2}$

Combine the numerators over the common denominator.

$- 3 x < \frac{- 3 + 2}{2}$

Add $- 3$ and $2$ .

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

Move the negative in front of the fraction.

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

Step 4

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

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

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

Simplify the left side.

Cancel the common factor of $- 3$ .

Cancel the common factor.

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

Divide $x$ by $1$ .

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

Simplify the right side.

Multiply the numerator by the reciprocal of the denominator.

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

Move the negative in front of the fraction.

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

Multiply $- \frac{1}{2} (- \frac{1}{3})$ .

Multiply $- 1$ by $- 1$ .

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

Multiply $\frac{1}{2}$ by $1$ .

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

Multiply $\frac{1}{2}$ by $\frac{1}{3}$ .

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

Multiply $2$ by $3$ .

$x > \frac{1}{6}$

Step 5

The result can be shown in multiple forms.

Inequality Form:

$x > \frac{1}{6}$

Interval Notation:

$(\frac{1}{6}, \infty)$

Solve for x 9x-1<3/4*(16x-2)

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