Algebra Examples

$\frac{2}{3} m + a = a + r$

Step 1

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

$\frac{2 m}{3} + a = a + r$

Step 2

Move all terms not containing $m$ to the right side of the equation.

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Step 2.1

Subtract $a$ from both sides of the equation.

$\frac{2 m}{3} = a + r - a$

Step 2.2

Combine the opposite terms in $a + r - a$ .

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Step 2.2.1

Subtract $a$ from $a$ .

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

Step 2.2.2

Add $r$ and $0$ .

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

Step 3

Multiply both sides of the equation by $\frac{3}{2}$ .

$\frac{3}{2} \cdot \frac{2 m}{3} = \frac{3}{2} r$

Step 4

Simplify both sides of the equation.

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Step 4.1

Simplify the left side.

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Step 4.1.1

Simplify $\frac{3}{2} \cdot \frac{2 m}{3}$ .

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Step 4.1.1.1

Cancel the common factor of $3$ .

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Step 4.1.1.1.1

Cancel the common factor.

$\frac{3}{2} \cdot \frac{2 m}{3} = \frac{3}{2} r$

Step 4.1.1.1.2

Rewrite the expression.

$\frac{1}{2} (2 m) = \frac{3}{2} r$

Step 4.1.1.2

Cancel the common factor of $2$ .

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Step 4.1.1.2.1

Factor $2$ out of $2 m$ .

$\frac{1}{2} (2 (m)) = \frac{3}{2} r$

Step 4.1.1.2.2

Cancel the common factor.

$\frac{1}{2} (2 m) = \frac{3}{2} r$

Step 4.1.1.2.3

Rewrite the expression.

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

Step 4.2

Simplify the right side.

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Step 4.2.1

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

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