Solve the Inequality for x 9x+2>6+3/2(7x-2)

$9 x + 2 > 6 + \frac{3}{2} (7 x - 2)$

Simplify $6 + \frac{3}{2} \cdot (7 x - 2)$ .

Simplify each term.

Apply the distributive property.

$9 x + 2 > 6 + \frac{3}{2} (7 x) + \frac{3}{2} \cdot - 2$

Multiply $\frac{3}{2} (7 x)$ .

Combine $7$ and $\frac{3}{2}$ .

$9 x + 2 > 6 + \frac{7 \cdot 3}{2} x + \frac{3}{2} \cdot - 2$

Multiply $7$ by $3$ .

$9 x + 2 > 6 + \frac{21}{2} x + \frac{3}{2} \cdot - 2$

Combine $\frac{21}{2}$ and $x$ .

$9 x + 2 > 6 + \frac{21 x}{2} + \frac{3}{2} \cdot - 2$

Cancel the common factor of $2$ .

Factor $2$ out of $- 2$ .

$9 x + 2 > 6 + \frac{21 x}{2} + \frac{3}{2} \cdot (2 (- 1))$

Cancel the common factor.

$9 x + 2 > 6 + \frac{21 x}{2} + \frac{3}{2} \cdot (2 \cdot - 1)$

Rewrite the expression.

$9 x + 2 > 6 + \frac{21 x}{2} + 3 \cdot - 1$

Multiply $3$ by $- 1$ .

$9 x + 2 > 6 + \frac{21 x}{2} - 3$

Subtract $3$ from $6$ .

$9 x + 2 > \frac{21 x}{2} + 3$

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

Subtract $\frac{21 x}{2}$ from both sides of the inequality.

$9 x + 2 - \frac{21 x}{2} > 3$

To write $9 x$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$9 x \cdot \frac{2}{2} - \frac{21 x}{2} + 2 > 3$

Combine $9 x$ and $\frac{2}{2}$ .

$\frac{9 x \cdot 2}{2} - \frac{21 x}{2} + 2 > 3$

Combine the numerators over the common denominator.

$\frac{9 x \cdot 2 - 21 x}{2} + 2 > 3$

Simplify each term.

Simplify the numerator.

Factor $3 x$ out of $9 x \cdot 2 - 21 x$ .

Factor $3 x$ out of $9 x \cdot 2$ .

$\frac{3 x (3 \cdot 2) - 21 x}{2} + 2 > 3$

Factor $3 x$ out of $- 21 x$ .

$\frac{3 x (3 \cdot 2) + 3 x (- 7)}{2} + 2 > 3$

Factor $3 x$ out of $3 x (3 \cdot 2) + 3 x (- 7)$ .

$\frac{3 x (3 \cdot 2 - 7)}{2} + 2 > 3$

Multiply $3$ by $2$ .

$\frac{3 x (6 - 7)}{2} + 2 > 3$

Subtract $7$ from $6$ .

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

Multiply $- 1$ by $3$ .

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

Move the negative in front of the fraction.

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

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

Subtract $2$ from both sides of the inequality.

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

Subtract $2$ from $3$ .

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

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

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

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

Simplify the left side.

Dividing two negative values results in a positive value.

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

Divide $\frac{3 x}{2}$ by $1$ .

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

Simplify the right side.

Divide $1$ by $- 1$ .

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

Multiply both sides by $2$ .

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

Simplify.

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

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

Rewrite the expression.

$3 x < - 1 \cdot 2$

Simplify the right side.

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:

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

Solve the Inequality for x 9x+2>6+3/2(7x-2)

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