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

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

Solve for x

$$x>-\frac{8}{3}$$

Solution Steps

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

$$-\frac{5}{2}\times 3x-\frac{5}{2}\times 4<6-3x\times 0.5$$

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

$$\frac{-5\times 3}{2}x-\frac{5}{2}\times 4<6-3x\times 0.5$$

Multiply -5 and 3 to get -15.

$$\frac{-15}{2}x-\frac{5}{2}\times 4<6-3x\times 0.5$$

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

$$-\frac{15}{2}x-\frac{5}{2}\times 4<6-3x\times 0.5$$

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

$$-\frac{15}{2}x+\frac{-5\times 4}{2}<6-3x\times 0.5$$

Multiply -5 and 4 to get -20.

$$-\frac{15}{2}x+\frac{-20}{2}<6-3x\times 0.5$$

Divide -20 by 2 to get -10.

$$-\frac{15}{2}x-10<6-3x\times 0.5$$

Multiply 3 and 0.5 to get 1.5.

$$-\frac{15}{2}x-10<6-1.5x$$

Add 1.5x to both sides.

$$-\frac{15}{2}x-10+1.5x<6$$

Combine -\frac{15}{2}x and 1.5x to get -6x.

$$-6x-10<6$$

Add 10 to both sides.

$$-6x<6+10$$

Add 6 and 10 to get 16.

$$-6x<16$$

Divide both sides by -6. Since -6 is negative, the inequality direction is changed.

$$x>\frac{16}{-6}$$

Reduce the fraction \frac{16}{-6} to lowest terms by extracting and canceling out 2.

$$x>-\frac{8}{3}$$