Solve for a (4a-4)/16-(3-5a)/24=1

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

Step 1

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

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

Factor $4$ out of $4 a$ .

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

Factor $4$ out of $- 4$ .

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

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

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

Cancel the common factors.

Factor $4$ out of $16$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

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

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

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

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

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

Multiply $4$ by $6$ .

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

Combine the numerators over the common denominator.

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

Simplify the numerator.

Apply the distributive property.

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

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

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

Multiply $- 1$ by $6$ .

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

Apply the distributive property.

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

Multiply $- 1$ by $3$ .

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

Multiply $- 5$ by $- 1$ .

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

Add $6 a$ and $5 a$ .

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

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.

Simplify the left side.

Cancel the common factor of $24$ .

Cancel the common factor.

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

Rewrite the expression.

$11 a - 9 = 1 \cdot 24$

Simplify the right side.

Multiply $24$ by $1$ .

$11 a - 9 = 24$

Step 4

Solve for $a$ .

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

Add $9$ to both sides of the equation.

$11 a = 24 + 9$

Add $24$ and $9$ .

$11 a = 33$

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

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

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

Simplify the left side.

Cancel the common factor of $11$ .

Cancel the common factor.

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

Divide $a$ by $1$ .

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

Simplify the right side.

Divide $33$ by $11$ .

$a = 3$

Solve for a (4a-4)/16-(3-5a)/24=1

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