Solve 3/2(s-2)+1>-2(s-4)

$$\frac { 3 } { 2 } ( s - 2 ) + 1 > - 2 ( s - 4 )$$

Solve for s

$$s>\frac{20}{7}$$

Solution Steps

Use the distributive property to multiply \frac{3}{2} by s-2.

$$\frac{3}{2}s+\frac{3}{2}\left(-2\right)+1>-2\left(s-4\right)$$

Express \frac{3}{2}\left(-2\right) as a single fraction.

$$\frac{3}{2}s+\frac{3\left(-2\right)}{2}+1>-2\left(s-4\right)$$

Multiply 3 and -2 to get -6.

$$\frac{3}{2}s+\frac{-6}{2}+1>-2\left(s-4\right)$$

Divide -6 by 2 to get -3.

$$\frac{3}{2}s-3+1>-2\left(s-4\right)$$

Add -3 and 1 to get -2.

$$\frac{3}{2}s-2>-2\left(s-4\right)$$

Use the distributive property to multiply -2 by s-4.

$$\frac{3}{2}s-2>-2s+8$$

Add 2s to both sides.

$$\frac{3}{2}s-2+2s>8$$

Combine \frac{3}{2}s and 2s to get \frac{7}{2}s.

$$\frac{7}{2}s-2>8$$

Add 2 to both sides.

$$\frac{7}{2}s>8+2$$

Add 8 and 2 to get 10.

$$\frac{7}{2}s>10$$

Multiply both sides by \frac{2}{7}, the reciprocal of \frac{7}{2}. Since \frac{7}{2} is positive, the inequality direction remains the same.

$$s>10\times \frac{2}{7}$$

Express 10\times \frac{2}{7} as a single fraction.

$$s>\frac{10\times 2}{7}$$

Multiply 10 and 2 to get 20.

$$s>\frac{20}{7}$$