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

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

Solve for x

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

Solution Steps

Use the distributive property to multiply -\frac{5}{2} by 3x+4.

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

Express -\frac{5}{2}\times 3 as a single fraction.

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

Multiply -5 and 3 to get -15.

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

Fraction \frac{-15}{2} can be rewritten as -\frac{15}{2} by extracting the negative sign.

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

Express -\frac{5}{2}\times 4 as a single fraction.

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

Multiply -5 and 4 to get -20.

$$-\frac{15}{2}x+\frac{-20}{2}<6-3x$$

Divide -20 by 2 to get -10.

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

Add 3x to both sides.

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

Combine -\frac{15}{2}x and 3x to get -\frac{9}{2}x.

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

Add 10 to both sides.

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

Add 6 and 10 to get 16.

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

Multiply both sides by -\frac{2}{9}, the reciprocal of -\frac{9}{2}. Since -\frac{9}{2} is negative, the inequality direction is changed.

$$x>16\left(-\frac{2}{9}\right)$$

Express 16\left(-\frac{2}{9}\right) as a single fraction.

$$x>\frac{16\left(-2\right)}{9}$$

Multiply 16 and -2 to get -32.

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

Fraction \frac{-32}{9} can be rewritten as -\frac{32}{9} by extracting the negative sign.

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