Precalculus Examples

$3 x + 2 = \frac{5 x - 11}{8 y}$

Step 1

Multiply both sides by $8 y$ .

$(3 x + 2) (8 y) = \frac{5 x - 11}{8 y} (8 y)$

Step 2

Simplify.

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Step 2.1

Simplify the left side.

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Step 2.1.1

Simplify $(3 x + 2) (8 y)$ .

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Step 2.1.1.1

Apply the distributive property.

$3 x (8 y) + 2 (8 y) = \frac{5 x - 11}{8 y} (8 y)$

Step 2.1.1.2

Simplify the expression.

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Step 2.1.1.2.1

Rewrite using the commutative property of multiplication.

$3 \cdot 8 x y + 2 (8 y) = \frac{5 x - 11}{8 y} (8 y)$

Step 2.1.1.2.2

Multiply $8$ by $2$ .

$3 \cdot 8 x y + 16 y = \frac{5 x - 11}{8 y} (8 y)$

Step 2.1.1.2.3

Multiply $3$ by $8$ .

$24 x y + 16 y = \frac{5 x - 11}{8 y} (8 y)$

Step 2.2

Simplify the right side.

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Step 2.2.1

Simplify $\frac{5 x - 11}{8 y} (8 y)$ .

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Step 2.2.1.1

Rewrite using the commutative property of multiplication.

$24 x y + 16 y = 8 \frac{5 x - 11}{8 y} y$

Step 2.2.1.2

Cancel the common factor of $8$ .

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Step 2.2.1.2.1

Factor $8$ out of $8 y$ .

$24 x y + 16 y = 8 \frac{5 x - 11}{8 (y)} y$

Step 2.2.1.2.2

Cancel the common factor.

$24 x y + 16 y = 8 \frac{5 x - 11}{8 y} y$

Step 2.2.1.2.3

Rewrite the expression.

$24 x y + 16 y = \frac{5 x - 11}{y} y$

Step 2.2.1.3

Cancel the common factor of $y$ .

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Step 2.2.1.3.1

Cancel the common factor.

$24 x y + 16 y = \frac{5 x - 11}{y} y$

Step 2.2.1.3.2

Rewrite the expression.

$24 x y + 16 y = 5 x - 11$

Step 3

Solve for $x$ .

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Step 3.1

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

$24 x y + 16 y - 5 x = - 11$

Step 3.2

Subtract $16 y$ from both sides of the equation.

$24 x y - 5 x = - 11 - 16 y$

Step 3.3

Factor $x$ out of $24 x y - 5 x$ .

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Step 3.3.1

Factor $x$ out of $24 x y$ .

$x (24 y) - 5 x = - 11 - 16 y$

Step 3.3.2

Factor $x$ out of $- 5 x$ .

$x (24 y) + x \cdot - 5 = - 11 - 16 y$

Step 3.3.3

Factor $x$ out of $x (24 y) + x \cdot - 5$ .

$x (24 y - 5) = - 11 - 16 y$

Step 3.4

Divide each term in $x (24 y - 5) = - 11 - 16 y$ by $24 y - 5$ and simplify.

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Step 3.4.1

Divide each term in $x (24 y - 5) = - 11 - 16 y$ by $24 y - 5$ .

$\frac{x (24 y - 5)}{24 y - 5} = \frac{- 11}{24 y - 5} + \frac{- 16 y}{24 y - 5}$

Step 3.4.2

Simplify the left side.

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Step 3.4.2.1

Cancel the common factor of $24 y - 5$ .

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Step 3.4.2.1.1

Cancel the common factor.

$\frac{x (24 y - 5)}{24 y - 5} = \frac{- 11}{24 y - 5} + \frac{- 16 y}{24 y - 5}$

Step 3.4.2.1.2

Divide $x$ by $1$ .

$x = \frac{- 11}{24 y - 5} + \frac{- 16 y}{24 y - 5}$

Step 3.4.3

Simplify the right side.

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Step 3.4.3.1

Combine the numerators over the common denominator.

$x = \frac{- 11 - 16 y}{24 y - 5}$

Step 3.4.3.2

Rewrite $- 11$ as $- 1 (11)$ .

$x = \frac{- 1 (11) - 16 y}{24 y - 5}$

Step 3.4.3.3

Factor $- 1$ out of $- 16 y$ .

$x = \frac{- 1 (11) - (16 y)}{24 y - 5}$

Step 3.4.3.4

Factor $- 1$ out of $- 1 (11) - (16 y)$ .

$x = \frac{- 1 (11 + 16 y)}{24 y - 5}$

Step 3.4.3.5

Move the negative in front of the fraction.

$x = - \frac{11 + 16 y}{24 y - 5}$