Algebra Examples

$- \frac{5}{3} a = \frac{1}{2} (\frac{2}{3} a - 2 + \frac{4}{3} a)$

Step 1

Since $a$ is on the right side of the equation, switch the sides so it is on the left side of the equation.

$\frac{1}{2} \cdot (\frac{2}{3} a - 2 + \frac{4}{3} a) = - \frac{5}{3} a$

Step 2

Simplify $\frac{1}{2} \cdot (\frac{2}{3} a - 2 + \frac{4}{3} a)$ .

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Step 2.1

Rewrite.

$0 + 0 + \frac{1}{2} \cdot (\frac{2}{3} a - 2 + \frac{4}{3} a) = - \frac{5}{3} a$

Step 2.2

Simplify by adding zeros.

$\frac{1}{2} \cdot (\frac{2}{3} a - 2 + \frac{4}{3} a) = - \frac{5}{3} a$

Step 2.3

Simplify each term.

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Step 2.3.1

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

$\frac{1}{2} \cdot (\frac{2 a}{3} - 2 + \frac{4}{3} a) = - \frac{5}{3} a$

Step 2.3.2

Combine $\frac{4}{3}$ and $a$ .

$\frac{1}{2} \cdot (\frac{2 a}{3} - 2 + \frac{4 a}{3}) = - \frac{5}{3} a$

Step 2.4

Simplify terms.

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Step 2.4.1

Combine the numerators over the common denominator.

$\frac{1}{2} \cdot (- 2 + \frac{2 a + 4 a}{3}) = - \frac{5}{3} a$

Step 2.4.2

Add $2 a$ and $4 a$ .

$\frac{1}{2} \cdot (- 2 + \frac{6 a}{3}) = - \frac{5}{3} a$

Step 2.4.3

Cancel the common factor of $6$ and $3$ .

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Step 2.4.3.1

Factor $3$ out of $6 a$ .

$\frac{1}{2} \cdot (- 2 + \frac{3 (2 a)}{3}) = - \frac{5}{3} a$

Step 2.4.3.2

Cancel the common factors.

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Step 2.4.3.2.1

Factor $3$ out of $3$ .

$\frac{1}{2} \cdot (- 2 + \frac{3 (2 a)}{3 (1)}) = - \frac{5}{3} a$

Step 2.4.3.2.2

Cancel the common factor.

$\frac{1}{2} \cdot (- 2 + \frac{3 (2 a)}{3 \cdot 1}) = - \frac{5}{3} a$

Step 2.4.3.2.3

Rewrite the expression.

$\frac{1}{2} \cdot (- 2 + \frac{2 a}{1}) = - \frac{5}{3} a$

Step 2.4.3.2.4

Divide $2 a$ by $1$ .

$\frac{1}{2} \cdot (- 2 + 2 a) = - \frac{5}{3} a$

Step 2.4.4

Apply the distributive property.

$\frac{1}{2} \cdot - 2 + \frac{1}{2} (2 a) = - \frac{5}{3} a$

Step 2.4.5

Cancel the common factor of $2$ .

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Step 2.4.5.1

Factor $2$ out of $- 2$ .

$\frac{1}{2} \cdot (2 (- 1)) + \frac{1}{2} (2 a) = - \frac{5}{3} a$

Step 2.4.5.2

Cancel the common factor.

$\frac{1}{2} \cdot (2 \cdot - 1) + \frac{1}{2} (2 a) = - \frac{5}{3} a$

Step 2.4.5.3

Rewrite the expression.

$- 1 + \frac{1}{2} (2 a) = - \frac{5}{3} a$

Step 2.4.6

Cancel the common factor of $2$ .

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Step 2.4.6.1

Factor $2$ out of $2 a$ .

$- 1 + \frac{1}{2} (2 (a)) = - \frac{5}{3} a$

Step 2.4.6.2

Cancel the common factor.

$- 1 + \frac{1}{2} (2 a) = - \frac{5}{3} a$

Step 2.4.6.3

Rewrite the expression.

$- 1 + a = - \frac{5}{3} a$

Step 3

Simplify $- \frac{5}{3} a$ .

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Step 3.1

Combine $a$ and $\frac{5}{3}$ .

$- 1 + a = - \frac{a \cdot 5}{3}$

Step 3.2

Move $5$ to the left of $a$ .

$- 1 + a = - \frac{5 a}{3}$

Step 4

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

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Step 4.1

Add $\frac{5 a}{3}$ to both sides of the equation.

$- 1 + a + \frac{5 a}{3} = 0$

Step 4.2

To write $a$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$- 1 + a \cdot \frac{3}{3} + \frac{5 a}{3} = 0$

Step 4.3

Combine $a$ and $\frac{3}{3}$ .

$- 1 + \frac{a \cdot 3}{3} + \frac{5 a}{3} = 0$

Step 4.4

Combine the numerators over the common denominator.

$- 1 + \frac{a \cdot 3 + 5 a}{3} = 0$

Step 4.5

Add $a \cdot 3$ and $5 a$ .

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Step 4.5.1

Reorder $a$ and $3$ .

$- 1 + \frac{3 \cdot a + 5 a}{3} = 0$

Step 4.5.2

Add $3 \cdot a$ and $5 a$ .

$- 1 + \frac{8 \cdot a}{3} = 0$

$- 1 + \frac{8 a}{3} = 0$

Step 5

Add $1$ to both sides of the equation.

$\frac{8 a}{3} = 1$

Step 6

Multiply both sides of the equation by $\frac{3}{8}$ .

$\frac{3}{8} \cdot \frac{8 a}{3} = \frac{3}{8} \cdot 1$

Step 7

Simplify both sides of the equation.

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Step 7.1

Simplify the left side.

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Step 7.1.1

Simplify $\frac{3}{8} \cdot \frac{8 a}{3}$ .

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Step 7.1.1.1

Cancel the common factor of $3$ .

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Step 7.1.1.1.1

Cancel the common factor.

$\frac{3}{8} \cdot \frac{8 a}{3} = \frac{3}{8} \cdot 1$

Step 7.1.1.1.2

Rewrite the expression.

$\frac{1}{8} (8 a) = \frac{3}{8} \cdot 1$

Step 7.1.1.2

Cancel the common factor of $8$ .

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Step 7.1.1.2.1

Factor $8$ out of $8 a$ .

$\frac{1}{8} (8 (a)) = \frac{3}{8} \cdot 1$

Step 7.1.1.2.2

Cancel the common factor.

$\frac{1}{8} (8 a) = \frac{3}{8} \cdot 1$

Step 7.1.1.2.3

Rewrite the expression.

$a = \frac{3}{8} \cdot 1$

Step 7.2

Simplify the right side.

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Step 7.2.1

Multiply $\frac{3}{8}$ by $1$ .

$a = \frac{3}{8}$

Step 8

The result can be shown in multiple forms.

Exact Form:

$a = \frac{3}{8}$

Decimal Form:

$a = 0.375$