Solve for y 5y+2=1/2(10y+4)

$5 y + 2 = \frac{1}{2} (10 y + 4)$

Step 1

Simplify $\frac{1}{2} \cdot (10 y + 4)$ .

Rewrite.

$5 y + 2 = 0 + 0 + \frac{1}{2} \cdot (10 y + 4)$

Simplify by adding zeros.

$5 y + 2 = \frac{1}{2} \cdot (10 y + 4)$

Apply the distributive property.

$5 y + 2 = \frac{1}{2} (10 y) + \frac{1}{2} \cdot 4$

Cancel the common factor of $2$ .

Factor $2$ out of $10 y$ .

$5 y + 2 = \frac{1}{2} (2 (5 y)) + \frac{1}{2} \cdot 4$

Cancel the common factor.

$5 y + 2 = \frac{1}{2} (2 (5 y)) + \frac{1}{2} \cdot 4$

Rewrite the expression.

$5 y + 2 = 5 y + \frac{1}{2} \cdot 4$

Cancel the common factor of $2$ .

Factor $2$ out of $4$ .

$5 y + 2 = 5 y + \frac{1}{2} \cdot (2 (2))$

Cancel the common factor.

$5 y + 2 = 5 y + \frac{1}{2} \cdot (2 \cdot 2)$

Rewrite the expression.

$5 y + 2 = 5 y + 2$

Step 2

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

Subtract $5 y$ from both sides of the equation.

$5 y + 2 - 5 y = 2$

Combine the opposite terms in $5 y + 2 - 5 y$ .

Subtract $5 y$ from $5 y$ .

$0 + 2 = 2$

Add $0$ and $2$ .

$2 = 2$

Step 3

Since $2 = 2$ , the equation will always be true for any value of $y$ .

All real numbers

Step 4

The result can be shown in multiple forms.

All real numbers

Interval Notation:

$(- \infty, \infty)$