Solve for x 1/2(8x+3)=4x+3/2

$\frac{1}{2} (8 x + 3) = 4 x + \frac{3}{2}$

Step 1

Simplify $\frac{1}{2} \cdot (8 x + 3)$ .

Rewrite.

$0 + 0 + \frac{1}{2} \cdot (8 x + 3) = 4 x + \frac{3}{2}$

Simplify by adding zeros.

$\frac{1}{2} \cdot (8 x + 3) = 4 x + \frac{3}{2}$

Apply the distributive property.

$\frac{1}{2} (8 x) + \frac{1}{2} \cdot 3 = 4 x + \frac{3}{2}$

Cancel the common factor of $2$ .

Factor $2$ out of $8 x$ .

$\frac{1}{2} (2 (4 x)) + \frac{1}{2} \cdot 3 = 4 x + \frac{3}{2}$

Cancel the common factor.

$\frac{1}{2} (2 (4 x)) + \frac{1}{2} \cdot 3 = 4 x + \frac{3}{2}$

Rewrite the expression.

$4 x + \frac{1}{2} \cdot 3 = 4 x + \frac{3}{2}$

Combine $\frac{1}{2}$ and $3$ .

$4 x + \frac{3}{2} = 4 x + \frac{3}{2}$

Step 2

Move all terms containing $x$ to the left side of the equation.

Subtract $4 x$ from both sides of the equation.

$4 x + \frac{3}{2} - 4 x = \frac{3}{2}$

Combine the opposite terms in $4 x + \frac{3}{2} - 4 x$ .

Subtract $4 x$ from $4 x$ .

$0 + \frac{3}{2} = \frac{3}{2}$

Add $0$ and $\frac{3}{2}$ .

$\frac{3}{2} = \frac{3}{2}$

Step 3

Since $\frac{3}{2} = \frac{3}{2}$ , the equation will always be true for any value of $x$ .

All real numbers

Step 4

The result can be shown in multiple forms.

All real numbers

Interval Notation:

$(- \infty, \infty)$