Solve the Inequality for x 1>1/2-3(-2x-1)+9x

$1 > \frac{1}{2} - 3 (- 2 x - 1) + 9 x$

Rewrite so $x$ is on the left side of the inequality.

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

Simplify $\frac{1}{2} - 3 (- 2 x - 1) + 9 x$ .

Simplify each term.

Apply the distributive property.

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

Multiply $- 2$ by $- 3$ .

$\frac{1}{2} + 6 x - 3 \cdot - 1 + 9 x < 1$

Multiply $- 3$ by $- 1$ .

$\frac{1}{2} + 6 x + 3 + 9 x < 1$

To write $3$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$6 x + \frac{1}{2} + 3 \cdot \frac{2}{2} + 9 x < 1$

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

$6 x + \frac{1}{2} + \frac{3 \cdot 2}{2} + 9 x < 1$

Combine the numerators over the common denominator.

$6 x + \frac{1 + 3 \cdot 2}{2} + 9 x < 1$

Simplify the numerator.

Multiply $3$ by $2$ .

$6 x + \frac{1 + 6}{2} + 9 x < 1$

Add $1$ and $6$ .

$6 x + \frac{7}{2} + 9 x < 1$

Add $6 x$ and $9 x$ .

$15 x + \frac{7}{2} < 1$

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

Subtract $\frac{7}{2}$ from both sides of the inequality.

$15 x < 1 - \frac{7}{2}$

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

$15 x < \frac{2}{2} - \frac{7}{2}$

Combine the numerators over the common denominator.

$15 x < \frac{2 - 7}{2}$

Subtract $7$ from $2$ .

$15 x < \frac{- 5}{2}$

Move the negative in front of the fraction.

$15 x < - \frac{5}{2}$

Divide each term in $15 x < - \frac{5}{2}$ by $15$ and simplify.

Divide each term in $15 x < - \frac{5}{2}$ by $15$ .

$\frac{15 x}{15} < \frac{- \frac{5}{2}}{15}$

Simplify the left side.

Cancel the common factor of $15$ .

Cancel the common factor.

$\frac{15 x}{15} < \frac{- \frac{5}{2}}{15}$

Divide $x$ by $1$ .

$x < \frac{- \frac{5}{2}}{15}$

Simplify the right side.

Multiply the numerator by the reciprocal of the denominator.

$x < - \frac{5}{2} \cdot \frac{1}{15}$

Cancel the common factor of $5$ .

Move the leading negative in $- \frac{5}{2}$ into the numerator.

$x < \frac{- 5}{2} \cdot \frac{1}{15}$

Factor $5$ out of $- 5$ .

$x < \frac{5 (- 1)}{2} \cdot \frac{1}{15}$

Factor $5$ out of $15$ .

$x < \frac{5 \cdot - 1}{2} \cdot \frac{1}{5 \cdot 3}$

Cancel the common factor.

$x < \frac{5 \cdot - 1}{2} \cdot \frac{1}{5 \cdot 3}$

Rewrite the expression.

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

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

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

Simplify the expression.

Multiply $2$ by $3$ .

$x < \frac{- 1}{6}$

Move the negative in front of the fraction.

$x < - \frac{1}{6}$

The result can be shown in multiple forms.

Inequality Form:

$x < - \frac{1}{6}$

Interval Notation:

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

Solve the Inequality for x 1>1/2-3(-2x-1)+9x

Related Questions

Support LCMGCF.com by disabling your adblocker.