Basic Math Examples

$\frac{3 a + 5 b - 2}{8 - a} = 4$

Step 1

Find the LCD of the terms in the equation.

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Step 1.1

Finding the LCD of a list of values is the same as finding the LCM of the denominators of those values.

$8 - a, 1$

Step 1.2

Remove parentheses.

$8 - a, 1$

Step 1.3

The LCM of one and any expression is the expression.

$8 - a$

Step 2

Multiply each term in $\frac{3 a + 5 b - 2}{8 - a} = 4$ by $8 - a$ to eliminate the fractions.

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Step 2.1

Multiply each term in $\frac{3 a + 5 b - 2}{8 - a} = 4$ by $8 - a$ .

$\frac{3 a + 5 b - 2}{8 - a} (8 - a) = 4 (8 - a)$

Step 2.2

Simplify the left side.

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Step 2.2.1

Cancel the common factor of $8 - a$ .

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Step 2.2.1.1

Cancel the common factor.

$\frac{3 a + 5 b - 2}{8 - a} (8 - a) = 4 (8 - a)$

Step 2.2.1.2

Rewrite the expression.

$3 a + 5 b - 2 = 4 (8 - a)$

Step 2.3

Simplify the right side.

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Step 2.3.1

Apply the distributive property.

$3 a + 5 b - 2 = 4 \cdot 8 + 4 (- a)$

Step 2.3.2

Multiply.

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Step 2.3.2.1

Multiply $4$ by $8$ .

$3 a + 5 b - 2 = 32 + 4 (- a)$

Step 2.3.2.2

Multiply $- 1$ by $4$ .

$3 a + 5 b - 2 = 32 - 4 a$

Step 3

Solve the equation.

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Step 3.1

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

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Step 3.1.1

Add $4 a$ to both sides of the equation.

$3 a + 5 b - 2 + 4 a = 32$

Step 3.1.2

Add $3 a$ and $4 a$ .

$7 a + 5 b - 2 = 32$

Step 3.2

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

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Step 3.2.1

Subtract $5 b$ from both sides of the equation.

$7 a - 2 = 32 - 5 b$

Step 3.2.2

Add $2$ to both sides of the equation.

$7 a = 32 - 5 b + 2$

Step 3.2.3

Add $32$ and $2$ .

$7 a = - 5 b + 34$

Step 3.3

Divide each term in $7 a = - 5 b + 34$ by $7$ and simplify.

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Step 3.3.1

Divide each term in $7 a = - 5 b + 34$ by $7$ .

$\frac{7 a}{7} = \frac{- 5 b}{7} + \frac{34}{7}$

Step 3.3.2

Simplify the left side.

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Step 3.3.2.1

Cancel the common factor of $7$ .

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Step 3.3.2.1.1

Cancel the common factor.

$\frac{7 a}{7} = \frac{- 5 b}{7} + \frac{34}{7}$

Step 3.3.2.1.2

Divide $a$ by $1$ .

$a = \frac{- 5 b}{7} + \frac{34}{7}$

Step 3.3.3

Simplify the right side.

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Step 3.3.3.1

Move the negative in front of the fraction.

$a = - \frac{5 b}{7} + \frac{34}{7}$