Solve 2(x-4)+1<3(2-x)

$$2 ( x - 4 ) + 1 < 3 ( 2 - x )$$

Solve for x

$$x<\frac{13}{5}$$

Solution Steps

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

$$2x-8+1<3\left(2-x\right)$$

Add -8 and 1 to get -7.

$$2x-7<3\left(2-x\right)$$

Use the distributive property to multiply 3 by 2-x.

$$2x-7<6-3x$$

Add 3x to both sides.

$$2x-7+3x<6$$

Combine 2x and 3x to get 5x.

$$5x-7<6$$

Add 7 to both sides.

$$5x<6+7$$

Add 6 and 7 to get 13.

$$5x<13$$

Divide both sides by 5. Since 5 is positive, the inequality direction remains the same.

$$x<\frac{13}{5}$$