Algebra Examples

$\frac{4 a - 4}{16} - \frac{3 - 5 a}{24} = 1$

Step 1

Simplify $\frac{4 a - 4}{16} - \frac{3 - 5 a}{24}$ .

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Step 1.1

Cancel the common factor of $4 a - 4$ and $16$ .

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Step 1.1.1

Factor $4$ out of $4 a$ .

$\frac{4 (a) - 4}{16} - \frac{3 - 5 a}{24} = 1$

Step 1.1.2

Factor $4$ out of $- 4$ .

$\frac{4 (a) + 4 (- 1)}{16} - \frac{3 - 5 a}{24} = 1$

Step 1.1.3

Factor $4$ out of $4 (a) + 4 (- 1)$ .

$\frac{4 (a - 1)}{16} - \frac{3 - 5 a}{24} = 1$

Step 1.1.4

Cancel the common factors.

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Step 1.1.4.1

Factor $4$ out of $16$ .

$\frac{4 (a - 1)}{4 (4)} - \frac{3 - 5 a}{24} = 1$

Step 1.1.4.2

Cancel the common factor.

$\frac{4 (a - 1)}{4 \cdot 4} - \frac{3 - 5 a}{24} = 1$

Step 1.1.4.3

Rewrite the expression.

$\frac{a - 1}{4} - \frac{3 - 5 a}{24} = 1$

Step 1.2

To write $\frac{a - 1}{4}$ as a fraction with a common denominator, multiply by $\frac{6}{6}$ .

$\frac{a - 1}{4} \cdot \frac{6}{6} - \frac{3 - 5 a}{24} = 1$

Step 1.3

Write each expression with a common denominator of $24$ , by multiplying each by an appropriate factor of $1$ .

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Step 1.3.1

Multiply $\frac{a - 1}{4}$ by $\frac{6}{6}$ .

$\frac{(a - 1) \cdot 6}{4 \cdot 6} - \frac{3 - 5 a}{24} = 1$

Step 1.3.2

Multiply $4$ by $6$ .

$\frac{(a - 1) \cdot 6}{24} - \frac{3 - 5 a}{24} = 1$

Step 1.4

Combine the numerators over the common denominator.

$\frac{(a - 1) \cdot 6 - (3 - 5 a)}{24} = 1$

Step 1.5

Simplify the numerator.

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Step 1.5.1

Apply the distributive property.

$\frac{a \cdot 6 - 1 \cdot 6 - (3 - 5 a)}{24} = 1$

Step 1.5.2

Move $6$ to the left of $a$ .

$\frac{6 \cdot a - 1 \cdot 6 - (3 - 5 a)}{24} = 1$

Step 1.5.3

Multiply $- 1$ by $6$ .

$\frac{6 \cdot a - 6 - (3 - 5 a)}{24} = 1$

Step 1.5.4

Apply the distributive property.

$\frac{6 a - 6 - 1 \cdot 3 - (- 5 a)}{24} = 1$

Step 1.5.5

Multiply $- 1$ by $3$ .

$\frac{6 a - 6 - 3 - (- 5 a)}{24} = 1$

Step 1.5.6

Multiply $- 5$ by $- 1$ .

$\frac{6 a - 6 - 3 + 5 a}{24} = 1$

Step 1.5.7

Add $6 a$ and $5 a$ .

$\frac{11 a - 6 - 3}{24} = 1$

Step 1.5.8

Subtract $3$ from $- 6$ .

$\frac{11 a - 9}{24} = 1$

Step 2

Multiply both sides by $24$ .

$\frac{11 a - 9}{24} \cdot 24 = 1 \cdot 24$

Step 3

Simplify.

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Step 3.1

Simplify the left side.

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Step 3.1.1

Cancel the common factor of $24$ .

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Step 3.1.1.1

Cancel the common factor.

$\frac{11 a - 9}{24} \cdot 24 = 1 \cdot 24$

Step 3.1.1.2

Rewrite the expression.

$11 a - 9 = 1 \cdot 24$

Step 3.2

Simplify the right side.

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Step 3.2.1

Multiply $24$ by $1$ .

$11 a - 9 = 24$

Step 4

Solve for $a$ .

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Step 4.1

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

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Step 4.1.1

Add $9$ to both sides of the equation.

$11 a = 24 + 9$

Step 4.1.2

Add $24$ and $9$ .

$11 a = 33$

Step 4.2

Divide each term in $11 a = 33$ by $11$ and simplify.

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Step 4.2.1

Divide each term in $11 a = 33$ by $11$ .

$\frac{11 a}{11} = \frac{33}{11}$

Step 4.2.2

Simplify the left side.

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Step 4.2.2.1

Cancel the common factor of $11$ .

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Step 4.2.2.1.1

Cancel the common factor.

$\frac{11 a}{11} = \frac{33}{11}$

Step 4.2.2.1.2

Divide $a$ by $1$ .

$a = \frac{33}{11}$

Step 4.2.3

Simplify the right side.

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Step 4.2.3.1

Divide $33$ by $11$ .

$a = 3$