Solve |x/2+1|=3/2

$$| \frac { x } { 2 } + 1 | = \frac { 3 } { 2 }$$

Solve for x

$$x=-5$$

$$x=1$$

Steps Using Definition of Absolute Value

Combine like terms and use the properties of equality to get the variable on one side of the equal sign and the numbers on the other side. Remember to follow the order of operations.

$$|\frac{1}{2}x+1|=\frac{3}{2}$$

Use the definition of absolute value.

$$\frac{1}{2}x+1=\frac{3}{2} \frac{1}{2}x+1=-\frac{3}{2}$$

Subtract 1 from both sides of the equation.

$$\frac{1}{2}x=\frac{1}{2} \frac{1}{2}x=-\frac{5}{2}$$

Multiply both sides by 2.

$$x=1 x=-5$$