Pre-Algebra Examples

$20 (\frac{1}{5} x + \frac{1}{4} y) = 20 (6)$

Step 1

Solve for $y$ .

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Step 1.1

Simplify $20 (\frac{1}{5} x + \frac{1}{4} y)$ .

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Step 1.1.1

Simplify each term.

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Step 1.1.1.1

Combine $\frac{1}{5}$ and $x$ .

$20 (\frac{x}{5} + \frac{1}{4} y) = 20 (6)$

Step 1.1.1.2

Combine $\frac{1}{4}$ and $y$ .

$20 (\frac{x}{5} + \frac{y}{4}) = 20 (6)$

$20 (\frac{x}{5} + \frac{y}{4}) = 20 (6)$

Step 1.1.2

Simplify terms.

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Step 1.1.2.1

Apply the distributive property.

$20 \frac{x}{5} + 20 \frac{y}{4} = 20 (6)$

Step 1.1.2.2

Cancel the common factor of $5$ .

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Step 1.1.2.2.1

Factor $5$ out of $20$ .

$5 (4) \frac{x}{5} + 20 \frac{y}{4} = 20 (6)$

Step 1.1.2.2.2

Cancel the common factor.

$5 \cdot 4 \frac{x}{5} + 20 \frac{y}{4} = 20 (6)$

Step 1.1.2.2.3

Rewrite the expression.

$4 x + 20 \frac{y}{4} = 20 (6)$

$4 x + 20 \frac{y}{4} = 20 (6)$

Step 1.1.2.3

Cancel the common factor of $4$ .

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Step 1.1.2.3.1

Factor $4$ out of $20$ .

$4 x + 4 (5) \frac{y}{4} = 20 (6)$

Step 1.1.2.3.2

Cancel the common factor.

$4 x + 4 \cdot 5 \frac{y}{4} = 20 (6)$

Step 1.1.2.3.3

Rewrite the expression.

$4 x + 5 y = 20 (6)$

$4 x + 5 y = 20 (6)$

$4 x + 5 y = 20 (6)$

$4 x + 5 y = 20 (6)$

Step 1.2

Multiply $20$ by $6$ .

$4 x + 5 y = 120$

Step 1.3

Subtract $4 x$ from both sides of the equation.

$5 y = 120 - 4 x$

Step 1.4

Divide each term in $5 y = 120 - 4 x$ by $5$ and simplify.

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Step 1.4.1

Divide each term in $5 y = 120 - 4 x$ by $5$ .

$\frac{5 y}{5} = \frac{120}{5} + \frac{- 4 x}{5}$

Step 1.4.2

Simplify the left side.

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Step 1.4.2.1

Cancel the common factor of $5$ .

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Step 1.4.2.1.1

Cancel the common factor.

$\frac{5 y}{5} = \frac{120}{5} + \frac{- 4 x}{5}$

Step 1.4.2.1.2

Divide $y$ by $1$ .

$y = \frac{120}{5} + \frac{- 4 x}{5}$

$y = \frac{120}{5} + \frac{- 4 x}{5}$

$y = \frac{120}{5} + \frac{- 4 x}{5}$

Step 1.4.3

Simplify the right side.

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Step 1.4.3.1

Simplify each term.

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Step 1.4.3.1.1

Divide $120$ by $5$ .

$y = 24 + \frac{- 4 x}{5}$

Step 1.4.3.1.2

Move the negative in front of the fraction.

$y = 24 - \frac{4 x}{5}$

$y = 24 - \frac{4 x}{5}$

$y = 24 - \frac{4 x}{5}$

$y = 24 - \frac{4 x}{5}$

$y = 24 - \frac{4 x}{5}$

Step 2

Reorder $24$ and $- \frac{4 x}{5}$ .

$y = - \frac{4 x}{5} + 24$

Step 3

Reorder terms.

$y = - (\frac{4}{5} x) + 24$

Step 4

Remove parentheses.

$y = - \frac{4}{5} x + 24$

Step 5

$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$