Pre-Algebra Examples

$\frac{2}{7} x - \frac{8}{5} = \frac{5 x + 3}{2}$

Step 1

Multiply both sides by $2$ .

$(\frac{2}{7} x - \frac{8}{5}) \cdot 2 = \frac{5 x + 3}{2} \cdot 2$

Step 2

Simplify.

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Step 2.1

Simplify the left side.

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Step 2.1.1

Simplify $(\frac{2}{7} x - \frac{8}{5}) \cdot 2$ .

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Step 2.1.1.1

Combine $\frac{2}{7}$ and $x$ .

$(\frac{2 x}{7} - \frac{8}{5}) \cdot 2 = \frac{5 x + 3}{2} \cdot 2$

Step 2.1.1.2

Apply the distributive property.

$\frac{2 x}{7} \cdot 2 - \frac{8}{5} \cdot 2 = \frac{5 x + 3}{2} \cdot 2$

Step 2.1.1.3

Multiply $\frac{2 x}{7} \cdot 2$ .

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Step 2.1.1.3.1

Combine $\frac{2 x}{7}$ and $2$ .

$\frac{2 x \cdot 2}{7} - \frac{8}{5} \cdot 2 = \frac{5 x + 3}{2} \cdot 2$

Step 2.1.1.3.2

Multiply $2$ by $2$ .

$\frac{4 x}{7} - \frac{8}{5} \cdot 2 = \frac{5 x + 3}{2} \cdot 2$

Step 2.1.1.4

Multiply $- \frac{8}{5} \cdot 2$ .

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Step 2.1.1.4.1

Multiply $2$ by $- 1$ .

$\frac{4 x}{7} - 2 (\frac{8}{5}) = \frac{5 x + 3}{2} \cdot 2$

Step 2.1.1.4.2

Combine $- 2$ and $\frac{8}{5}$ .

$\frac{4 x}{7} + \frac{- 2 \cdot 8}{5} = \frac{5 x + 3}{2} \cdot 2$

Step 2.1.1.4.3

Multiply $- 2$ by $8$ .

$\frac{4 x}{7} + \frac{- 16}{5} = \frac{5 x + 3}{2} \cdot 2$

Step 2.1.1.5

Move the negative in front of the fraction.

$\frac{4 x}{7} - \frac{16}{5} = \frac{5 x + 3}{2} \cdot 2$

Step 2.2

Simplify the right side.

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Step 2.2.1

Cancel the common factor of $2$ .

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Step 2.2.1.1

Cancel the common factor.

$\frac{4 x}{7} - \frac{16}{5} = \frac{5 x + 3}{2} \cdot 2$

Step 2.2.1.2

Rewrite the expression.

$\frac{4 x}{7} - \frac{16}{5} = 5 x + 3$

Step 3

Solve for $x$ .

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Step 3.1

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

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Step 3.1.1

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

$\frac{4 x}{7} - \frac{16}{5} - 5 x = 3$

Step 3.1.2

To write $- 5 x$ as a fraction with a common denominator, multiply by $\frac{7}{7}$ .

$\frac{4 x}{7} - 5 x \cdot \frac{7}{7} - \frac{16}{5} = 3$

Step 3.1.3

Combine $- 5 x$ and $\frac{7}{7}$ .

$\frac{4 x}{7} + \frac{- 5 x \cdot 7}{7} - \frac{16}{5} = 3$

Step 3.1.4

Combine the numerators over the common denominator.

$\frac{4 x - 5 x \cdot 7}{7} - \frac{16}{5} = 3$

Step 3.1.5

Simplify each term.

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Step 3.1.5.1

Simplify the numerator.

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Step 3.1.5.1.1

Factor $x$ out of $4 x - 5 x \cdot 7$ .

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Step 3.1.5.1.1.1

Factor $x$ out of $4 x$ .

$\frac{x \cdot 4 - 5 x \cdot 7}{7} - \frac{16}{5} = 3$

Step 3.1.5.1.1.2

Factor $x$ out of $- 5 x \cdot 7$ .

$\frac{x \cdot 4 + x (- 5 \cdot 7)}{7} - \frac{16}{5} = 3$

Step 3.1.5.1.1.3

Factor $x$ out of $x \cdot 4 + x (- 5 \cdot 7)$ .

$\frac{x (4 - 5 \cdot 7)}{7} - \frac{16}{5} = 3$

Step 3.1.5.1.2

Multiply $- 5$ by $7$ .

$\frac{x (4 - 35)}{7} - \frac{16}{5} = 3$

Step 3.1.5.1.3

Subtract $35$ from $4$ .

$\frac{x \cdot - 31}{7} - \frac{16}{5} = 3$

Step 3.1.5.2

Move $- 31$ to the left of $x$ .

$\frac{- 31 \cdot x}{7} - \frac{16}{5} = 3$

Step 3.1.5.3

Move the negative in front of the fraction.

$- \frac{31 x}{7} - \frac{16}{5} = 3$

Step 3.2

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

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Step 3.2.1

Add $\frac{16}{5}$ to both sides of the equation.

$- \frac{31 x}{7} = 3 + \frac{16}{5}$

Step 3.2.2

To write $3$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$- \frac{31 x}{7} = 3 \cdot \frac{5}{5} + \frac{16}{5}$

Step 3.2.3

Combine $3$ and $\frac{5}{5}$ .

$- \frac{31 x}{7} = \frac{3 \cdot 5}{5} + \frac{16}{5}$

Step 3.2.4

Combine the numerators over the common denominator.

$- \frac{31 x}{7} = \frac{3 \cdot 5 + 16}{5}$

Step 3.2.5

Simplify the numerator.

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Step 3.2.5.1

Multiply $3$ by $5$ .

$- \frac{31 x}{7} = \frac{15 + 16}{5}$

Step 3.2.5.2

Add $15$ and $16$ .

$- \frac{31 x}{7} = \frac{31}{5}$

Step 3.3

Multiply both sides of the equation by $- \frac{7}{31}$ .

$- \frac{7}{31} (- \frac{31 x}{7}) = - \frac{7}{31} \cdot \frac{31}{5}$

Step 3.4

Simplify both sides of the equation.

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Step 3.4.1

Simplify the left side.

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Step 3.4.1.1

Simplify $- \frac{7}{31} (- \frac{31 x}{7})$ .

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Step 3.4.1.1.1

Cancel the common factor of $7$ .

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Step 3.4.1.1.1.1

Move the leading negative in $- \frac{7}{31}$ into the numerator.

$\frac{- 7}{31} (- \frac{31 x}{7}) = - \frac{7}{31} \cdot \frac{31}{5}$

Step 3.4.1.1.1.2

Move the leading negative in $- \frac{31 x}{7}$ into the numerator.

$\frac{- 7}{31} \cdot \frac{- 31 x}{7} = - \frac{7}{31} \cdot \frac{31}{5}$

Step 3.4.1.1.1.3

Factor $7$ out of $- 7$ .

$\frac{7 (- 1)}{31} \cdot \frac{- 31 x}{7} = - \frac{7}{31} \cdot \frac{31}{5}$

Step 3.4.1.1.1.4

Cancel the common factor.

$\frac{7 \cdot - 1}{31} \cdot \frac{- 31 x}{7} = - \frac{7}{31} \cdot \frac{31}{5}$

Step 3.4.1.1.1.5

Rewrite the expression.

$\frac{- 1}{31} (- 31 x) = - \frac{7}{31} \cdot \frac{31}{5}$

Step 3.4.1.1.2

Cancel the common factor of $31$ .

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Step 3.4.1.1.2.1

Factor $31$ out of $- 31 x$ .

$\frac{- 1}{31} (31 (- x)) = - \frac{7}{31} \cdot \frac{31}{5}$

Step 3.4.1.1.2.2

Cancel the common factor.

$\frac{- 1}{31} (31 (- x)) = - \frac{7}{31} \cdot \frac{31}{5}$

Step 3.4.1.1.2.3

Rewrite the expression.

$- - x = - \frac{7}{31} \cdot \frac{31}{5}$

Step 3.4.1.1.3

Multiply.

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Step 3.4.1.1.3.1

Multiply $- 1$ by $- 1$ .

$1 x = - \frac{7}{31} \cdot \frac{31}{5}$

Step 3.4.1.1.3.2

Multiply $x$ by $1$ .

$x = - \frac{7}{31} \cdot \frac{31}{5}$

Step 3.4.2

Simplify the right side.

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Step 3.4.2.1

Simplify $- \frac{7}{31} \cdot \frac{31}{5}$ .

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Step 3.4.2.1.1

Cancel the common factor of $31$ .

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Step 3.4.2.1.1.1

Move the leading negative in $- \frac{7}{31}$ into the numerator.

$x = \frac{- 7}{31} \cdot \frac{31}{5}$

Step 3.4.2.1.1.2

Cancel the common factor.

$x = \frac{- 7}{31} \cdot \frac{31}{5}$

Step 3.4.2.1.1.3

Rewrite the expression.

$x = - 7 (\frac{1}{5})$

Step 3.4.2.1.2

Combine $- 7$ and $\frac{1}{5}$ .

$x = \frac{- 7}{5}$

Step 3.4.2.1.3

Move the negative in front of the fraction.

$x = - \frac{7}{5}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$x = - \frac{7}{5}$

Decimal Form:

$x = - 1.4$

Mixed Number Form:

$x = - 1 \frac{2}{5}$