Pre-Algebra Examples

$2 (\frac{4 y}{3}) + 7 y + \frac{22}{3} = 5$

Step 1

Simplify $2 (\frac{4 y}{3}) + 7 y + \frac{22}{3}$ .

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Step 1.1

Multiply $2 (\frac{4 y}{3})$ .

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Step 1.1.1

Combine $2$ and $\frac{4 y}{3}$ .

$\frac{2 (4 y)}{3} + 7 y + \frac{22}{3} = 5$

Step 1.1.2

Multiply $4$ by $2$ .

$\frac{8 y}{3} + 7 y + \frac{22}{3} = 5$

Step 1.2

To write $7 y$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$\frac{8 y}{3} + 7 y \cdot \frac{3}{3} + \frac{22}{3} = 5$

Step 1.3

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

$\frac{8 y}{3} + \frac{7 y \cdot 3}{3} + \frac{22}{3} = 5$

Step 1.4

Combine the numerators over the common denominator.

$\frac{8 y + 7 y \cdot 3}{3} + \frac{22}{3} = 5$

Step 1.5

Combine the numerators over the common denominator.

$\frac{8 y + 7 y \cdot 3 + 22}{3} = 5$

Step 1.6

Multiply $3$ by $7$ .

$\frac{8 y + 21 y + 22}{3} = 5$

Step 1.7

Add $8 y$ and $21 y$ .

$\frac{29 y + 22}{3} = 5$

Step 2

Multiply both sides by $3$ .

$\frac{29 y + 22}{3} \cdot 3 = 5 \cdot 3$

Step 3

Simplify.

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Step 3.1

Simplify the left side.

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Step 3.1.1

Cancel the common factor of $3$ .

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Step 3.1.1.1

Cancel the common factor.

$\frac{29 y + 22}{3} \cdot 3 = 5 \cdot 3$

Step 3.1.1.2

Rewrite the expression.

$29 y + 22 = 5 \cdot 3$

Step 3.2

Simplify the right side.

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Step 3.2.1

Multiply $5$ by $3$ .

$29 y + 22 = 15$

Step 4

Solve for $y$ .

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Step 4.1

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

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Step 4.1.1

Subtract $22$ from both sides of the equation.

$29 y = 15 - 22$

Step 4.1.2

Subtract $22$ from $15$ .

$29 y = - 7$

Step 4.2

Divide each term in $29 y = - 7$ by $29$ and simplify.

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Step 4.2.1

Divide each term in $29 y = - 7$ by $29$ .

$\frac{29 y}{29} = \frac{- 7}{29}$

Step 4.2.2

Simplify the left side.

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Step 4.2.2.1

Cancel the common factor of $29$ .

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Step 4.2.2.1.1

Cancel the common factor.

$\frac{29 y}{29} = \frac{- 7}{29}$

Step 4.2.2.1.2

Divide $y$ by $1$ .

$y = \frac{- 7}{29}$

Step 4.2.3

Simplify the right side.

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Step 4.2.3.1

Move the negative in front of the fraction.

$y = - \frac{7}{29}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$y = - \frac{7}{29}$

Decimal Form:

$y = - 0.24137931 \dots$