Solve the Inequality for x -5/2(3x+4)<6-3x

$- \frac{5}{2} (3 x + 4) < 6 - 3 x$

Step 1

Simplify $- \frac{5}{2} \cdot (3 x + 4)$ .

Rewrite.

$0 + 0 - \frac{5}{2} \cdot (3 x + 4) < 6 - 3 x$

Simplify by adding zeros.

$- \frac{5}{2} \cdot (3 x + 4) < 6 - 3 x$

Apply the distributive property.

$- \frac{5}{2} (3 x) - \frac{5}{2} \cdot 4 < 6 - 3 x$

Multiply $- \frac{5}{2} (3 x)$ .

Multiply $3$ by $- 1$ .

$- 3 (\frac{5}{2}) x - \frac{5}{2} \cdot 4 < 6 - 3 x$

Combine $- 3$ and $\frac{5}{2}$ .

$\frac{- 3 \cdot 5}{2} x - \frac{5}{2} \cdot 4 < 6 - 3 x$

Multiply $- 3$ by $5$ .

$\frac{- 15}{2} x - \frac{5}{2} \cdot 4 < 6 - 3 x$

Combine $\frac{- 15}{2}$ and $x$ .

$\frac{- 15 x}{2} - \frac{5}{2} \cdot 4 < 6 - 3 x$

Reduce the expression by cancelling the common factors.

Cancel the common factor of $2$ .

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

$\frac{- 15 x}{2} + \frac{- 5}{2} \cdot 4 < 6 - 3 x$

Factor $2$ out of $4$ .

$\frac{- 15 x}{2} + \frac{- 5}{2} \cdot (2 (2)) < 6 - 3 x$

Cancel the common factor.

$\frac{- 15 x}{2} + \frac{- 5}{2} \cdot (2 \cdot 2) < 6 - 3 x$

Rewrite the expression.

$\frac{- 15 x}{2} - 5 \cdot 2 < 6 - 3 x$

Multiply $- 5$ by $2$ .

$\frac{- 15 x}{2} - 10 < 6 - 3 x$

Move the negative in front of the fraction.

$- \frac{15 x}{2} - 10 < 6 - 3 x$

Step 2

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

Add $3 x$ to both sides of the inequality.

$- \frac{15 x}{2} - 10 + 3 x < 6$

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

$- \frac{15 x}{2} + 3 x \cdot \frac{2}{2} - 10 < 6$

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

$- \frac{15 x}{2} + \frac{3 x \cdot 2}{2} - 10 < 6$

Combine the numerators over the common denominator.

$\frac{- 15 x + 3 x \cdot 2}{2} - 10 < 6$

Simplify each term.

Simplify the numerator.

Factor $3 x$ out of $- 15 x + 3 x \cdot 2$ .

Factor $3 x$ out of $- 15 x$ .

$\frac{3 x (- 5) + 3 x \cdot 2}{2} - 10 < 6$

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

$\frac{3 x (- 5) + 3 x (2)}{2} - 10 < 6$

Factor $3 x$ out of $3 x (- 5) + 3 x (2)$ .

$\frac{3 x (- 5 + 2)}{2} - 10 < 6$

Add $- 5$ and $2$ .

$\frac{3 x \cdot - 3}{2} - 10 < 6$

Multiply $- 3$ by $3$ .

$\frac{- 9 x}{2} - 10 < 6$

Move the negative in front of the fraction.

$- \frac{9 x}{2} - 10 < 6$

Step 3

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

Add $10$ to both sides of the inequality.

$- \frac{9 x}{2} < 6 + 10$

Add $6$ and $10$ .

$- \frac{9 x}{2} < 16$

Step 4

Divide each term in $- \frac{9 x}{2} < 16$ by $- 1$ and simplify.

Divide each term in $- \frac{9 x}{2} < 16$ by $- 1$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- \frac{9 x}{2}}{- 1} > \frac{16}{- 1}$

Simplify the left side.

Dividing two negative values results in a positive value.

$\frac{\frac{9 x}{2}}{1} > \frac{16}{- 1}$

Divide $\frac{9 x}{2}$ by $1$ .

$\frac{9 x}{2} > \frac{16}{- 1}$

Simplify the right side.

Divide $16$ by $- 1$ .

$\frac{9 x}{2} > - 16$

Step 5

Multiply both sides by $2$ .

$\frac{9 x}{2} \cdot 2 > - 16 \cdot 2$

Step 6

Simplify.

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{9 x}{2} \cdot 2 > - 16 \cdot 2$

Rewrite the expression.

$9 x > - 16 \cdot 2$

Simplify the right side.

Multiply $- 16$ by $2$ .

$9 x > - 32$

Step 7

Divide each term in $9 x > - 32$ by $9$ and simplify.

Divide each term in $9 x > - 32$ by $9$ .

$\frac{9 x}{9} > \frac{- 32}{9}$

Simplify the left side.

Cancel the common factor of $9$ .

Cancel the common factor.

$\frac{9 x}{9} > \frac{- 32}{9}$

Divide $x$ by $1$ .

$x > \frac{- 32}{9}$

Simplify the right side.

Move the negative in front of the fraction.

$x > - \frac{32}{9}$

Step 8

The result can be shown in multiple forms.

Inequality Form:

$x > - \frac{32}{9}$

Interval Notation:

$(- \frac{32}{9}, \infty)$

Solve the Inequality for x -5/2(3x+4)<6-3x

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