Pre-Algebra Examples

$\frac{5 y - 2}{7} = \frac{3}{4}$

Step 1

Rewrite in slope-intercept form.

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Step 1.1

The slope-intercept form is $y = m x + b$ , where $m$ is the slope and $b$ is the y-intercept.

$y = m x + b$

Step 1.2

Multiply both sides by $7$ .

$\frac{5 y - 2}{7} \cdot 7 = \frac{3}{4} \cdot 7$

Step 1.3

Simplify.

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Step 1.3.1

Simplify the left side.

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Step 1.3.1.1

Cancel the common factor of $7$ .

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Step 1.3.1.1.1

Cancel the common factor.

$\frac{5 y - 2}{7} \cdot 7 = \frac{3}{4} \cdot 7$

Step 1.3.1.1.2

Rewrite the expression.

$5 y - 2 = \frac{3}{4} \cdot 7$

Step 1.3.2

Simplify the right side.

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Step 1.3.2.1

Multiply $\frac{3}{4} \cdot 7$ .

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Step 1.3.2.1.1

Combine $\frac{3}{4}$ and $7$ .

$5 y - 2 = \frac{3 \cdot 7}{4}$

Step 1.3.2.1.2

Multiply $3$ by $7$ .

$5 y - 2 = \frac{21}{4}$

Step 1.4

Solve for $y$ .

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Step 1.4.1

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

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Step 1.4.1.1

Add $2$ to both sides of the equation.

$5 y = \frac{21}{4} + 2$

Step 1.4.1.2

To write $2$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$5 y = \frac{21}{4} + 2 \cdot \frac{4}{4}$

Step 1.4.1.3

Combine $2$ and $\frac{4}{4}$ .

$5 y = \frac{21}{4} + \frac{2 \cdot 4}{4}$

Step 1.4.1.4

Combine the numerators over the common denominator.

$5 y = \frac{21 + 2 \cdot 4}{4}$

Step 1.4.1.5

Simplify the numerator.

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Step 1.4.1.5.1

Multiply $2$ by $4$ .

$5 y = \frac{21 + 8}{4}$

Step 1.4.1.5.2

Add $21$ and $8$ .

$5 y = \frac{29}{4}$

Step 1.4.2

Divide each term in $5 y = \frac{29}{4}$ by $5$ and simplify.

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Step 1.4.2.1

Divide each term in $5 y = \frac{29}{4}$ by $5$ .

$\frac{5 y}{5} = \frac{\frac{29}{4}}{5}$

Step 1.4.2.2

Simplify the left side.

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Step 1.4.2.2.1

Cancel the common factor of $5$ .

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Step 1.4.2.2.1.1

Cancel the common factor.

$\frac{5 y}{5} = \frac{\frac{29}{4}}{5}$

Step 1.4.2.2.1.2

Divide $y$ by $1$ .

$y = \frac{\frac{29}{4}}{5}$

Step 1.4.2.3

Simplify the right side.

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Step 1.4.2.3.1

Multiply the numerator by the reciprocal of the denominator.

$y = \frac{29}{4} \cdot \frac{1}{5}$

Step 1.4.2.3.2

Multiply $\frac{29}{4} \cdot \frac{1}{5}$ .

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Step 1.4.2.3.2.1

Multiply $\frac{29}{4}$ by $\frac{1}{5}$ .

$y = \frac{29}{4 \cdot 5}$

Step 1.4.2.3.2.2

Multiply $4$ by $5$ .

$y = \frac{29}{20}$

Step 2

Using the slope-intercept form, the slope is $0$ .

$m = 0$

Step 3