To solve an equation, we should first gather all of the variable terms on one side of the equation and all of the constant terms on the other side using the Properties of Equality.

\frac{1}{2} = \frac{1}{2} c - 2

$LHS + 2 = RHS + 2$

\frac{1}{2} + 2 = \frac{1}{2} c - 2 + 2

Add terms

\frac{1}{2} + 2 = \frac{1}{2} c

Rearrange equation

\frac{1}{2} c = \frac{1}{2} + 2

Now we can continue to solve using the Properties of Equality.

\frac{1}{2} c = \frac{1}{2} + 2

$LHS \cdot 2 = RHS \cdot 2$

2 (\frac{1}{2} c) = 2 (\frac{1}{2} + 2)

Distribute $2$

2 (\frac{1}{2} c) = 2 (\frac{1}{2}) + 2 (2)

$a \cdot \frac{b}{c} = \frac{a \cdot b}{c}$

\frac{2 ( 1 )}{2} c = \frac{2 ( 1 )}{2} + 2 (2)

\frac{2}{2} c = \frac{2}{2} + 4

Calculate quotient

c = 1 + 4

Add terms

c = 5

The solution to the equation is

c = 5 .

We can check our solution by substituting it into the original equation.

\frac{1}{2} = \frac{1}{2} c - 2

$c = 5$

\frac{1}{2} = ? \frac{1}{2} (5) - 2

▼

Evaluate

$\frac{a}{c} \cdot b = \frac{a \cdot b}{c}$

\frac{1}{2} = ? \frac{1 ( 5 )}{2} - 2

Calculate quotient

0.5 = ? 2.5 - 2

Subtract term

0.5 = 0.5

Since the left-hand side is equal to the right-hand side, our solution is correct.

{{ 'ml-heading-exercise' | message }} {{ exercise.name }} {{ 'ml-label-page' | message }} {{ exercise.page }}