Solve 3/2(x-2)<3/4(x-8)

$$\frac{ 3 }{ 2 } (x-2) < \frac{ 3 }{ 4 } (x-8)$$

Solve for x

$$x<-4$$

Solution Steps

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

$$\frac{3}{2}x+\frac{3}{2}\left(-2\right)<\frac{3}{4}\left(x-8\right)$$

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

$$\frac{3}{2}x+\frac{3\left(-2\right)}{2}<\frac{3}{4}\left(x-8\right)$$

Multiply 3 and -2 to get -6.

$$\frac{3}{2}x+\frac{-6}{2}<\frac{3}{4}\left(x-8\right)$$

Divide -6 by 2 to get -3.

$$\frac{3}{2}x-3<\frac{3}{4}\left(x-8\right)$$

Use the distributive property to multiply \frac{3}{4} by x-8.

$$\frac{3}{2}x-3<\frac{3}{4}x+\frac{3}{4}\left(-8\right)$$

Express \frac{3}{4}\left(-8\right) as a single fraction.

$$\frac{3}{2}x-3<\frac{3}{4}x+\frac{3\left(-8\right)}{4}$$

Multiply 3 and -8 to get -24.

$$\frac{3}{2}x-3<\frac{3}{4}x+\frac{-24}{4}$$

Divide -24 by 4 to get -6.

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

Subtract \frac{3}{4}x from both sides.

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

Combine \frac{3}{2}x and -\frac{3}{4}x to get \frac{3}{4}x.

$$\frac{3}{4}x-3<-6$$

Add 3 to both sides.

$$\frac{3}{4}x<-6+3$$

Add -6 and 3 to get -3.

$$\frac{3}{4}x<-3$$

Multiply both sides by \frac{4}{3}, the reciprocal of \frac{3}{4}. Since \frac{3}{4} is positive, the inequality direction remains the same.

$$x<-3\times \frac{4}{3}$$

Multiply -3 times \frac{4}{3}.

$$x<-4$$