Pre-Algebra Examples

$7 x + \frac{14}{3} - 17 - \frac{3 x}{5} = 6 x - 4 x + 23 - 5$

Step 1

Simplify $7 x + \frac{14}{3} - 17 - \frac{3 x}{5}$ .

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Step 1.1

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

$7 x \cdot \frac{5}{5} - \frac{3 x}{5} + \frac{14}{3} - 17 = 6 x - 4 x + 23 - 5$

Step 1.2

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

$\frac{7 x \cdot 5}{5} - \frac{3 x}{5} + \frac{14}{3} - 17 = 6 x - 4 x + 23 - 5$

Step 1.3

Combine the numerators over the common denominator.

$\frac{7 x \cdot 5 - 3 x}{5} + \frac{14}{3} - 17 = 6 x - 4 x + 23 - 5$

Step 1.4

Find the common denominator.

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Step 1.4.1

Multiply $\frac{7 x \cdot 5 - 3 x}{5}$ by $\frac{3}{3}$ .

$\frac{7 x \cdot 5 - 3 x}{5} \cdot \frac{3}{3} + \frac{14}{3} - 17 = 6 x - 4 x + 23 - 5$

Step 1.4.2

Multiply $\frac{7 x \cdot 5 - 3 x}{5}$ by $\frac{3}{3}$ .

$\frac{(7 x \cdot 5 - 3 x) \cdot 3}{5 \cdot 3} + \frac{14}{3} - 17 = 6 x - 4 x + 23 - 5$

Step 1.4.3

Multiply $\frac{14}{3}$ by $\frac{5}{5}$ .

$\frac{(7 x \cdot 5 - 3 x) \cdot 3}{5 \cdot 3} + \frac{14}{3} \cdot \frac{5}{5} - 17 = 6 x - 4 x + 23 - 5$

Step 1.4.4

Multiply $\frac{14}{3}$ by $\frac{5}{5}$ .

$\frac{(7 x \cdot 5 - 3 x) \cdot 3}{5 \cdot 3} + \frac{14 \cdot 5}{3 \cdot 5} - 17 = 6 x - 4 x + 23 - 5$

Step 1.4.5

Write $- 17$ as a fraction with denominator $1$ .

$\frac{(7 x \cdot 5 - 3 x) \cdot 3}{5 \cdot 3} + \frac{14 \cdot 5}{3 \cdot 5} + \frac{- 17}{1} = 6 x - 4 x + 23 - 5$

Step 1.4.6

Multiply $\frac{- 17}{1}$ by $\frac{15}{15}$ .

$\frac{(7 x \cdot 5 - 3 x) \cdot 3}{5 \cdot 3} + \frac{14 \cdot 5}{3 \cdot 5} + \frac{- 17}{1} \cdot \frac{15}{15} = 6 x - 4 x + 23 - 5$

Step 1.4.7

Multiply $\frac{- 17}{1}$ by $\frac{15}{15}$ .

$\frac{(7 x \cdot 5 - 3 x) \cdot 3}{5 \cdot 3} + \frac{14 \cdot 5}{3 \cdot 5} + \frac{- 17 \cdot 15}{15} = 6 x - 4 x + 23 - 5$

Step 1.4.8

Reorder the factors of $5 \cdot 3$ .

$\frac{(7 x \cdot 5 - 3 x) \cdot 3}{3 \cdot 5} + \frac{14 \cdot 5}{3 \cdot 5} + \frac{- 17 \cdot 15}{15} = 6 x - 4 x + 23 - 5$

Step 1.4.9

Multiply $3$ by $5$ .

$\frac{(7 x \cdot 5 - 3 x) \cdot 3}{15} + \frac{14 \cdot 5}{3 \cdot 5} + \frac{- 17 \cdot 15}{15} = 6 x - 4 x + 23 - 5$

Step 1.4.10

Multiply $3$ by $5$ .

$\frac{(7 x \cdot 5 - 3 x) \cdot 3}{15} + \frac{14 \cdot 5}{15} + \frac{- 17 \cdot 15}{15} = 6 x - 4 x + 23 - 5$

Step 1.5

Combine the numerators over the common denominator.

$\frac{(7 x \cdot 5 - 3 x) \cdot 3 + 14 \cdot 5 - 17 \cdot 15}{15} = 6 x - 4 x + 23 - 5$

Step 1.6

Simplify each term.

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Step 1.6.1

Multiply $5$ by $7$ .

$\frac{(35 x - 3 x) \cdot 3 + 14 \cdot 5 - 17 \cdot 15}{15} = 6 x - 4 x + 23 - 5$

Step 1.6.2

Subtract $3 x$ from $35 x$ .

$\frac{32 x \cdot 3 + 14 \cdot 5 - 17 \cdot 15}{15} = 6 x - 4 x + 23 - 5$

Step 1.6.3

Multiply $3$ by $32$ .

$\frac{96 x + 14 \cdot 5 - 17 \cdot 15}{15} = 6 x - 4 x + 23 - 5$

Step 1.6.4

Multiply $14$ by $5$ .

$\frac{96 x + 70 - 17 \cdot 15}{15} = 6 x - 4 x + 23 - 5$

Step 1.6.5

Multiply $- 17$ by $15$ .

$\frac{96 x + 70 - 255}{15} = 6 x - 4 x + 23 - 5$

Step 1.7

Subtract $255$ from $70$ .

$\frac{96 x - 185}{15} = 6 x - 4 x + 23 - 5$

Step 2

Simplify $6 x - 4 x + 23 - 5$ .

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Step 2.1

Subtract $4 x$ from $6 x$ .

$\frac{96 x - 185}{15} = 2 x + 23 - 5$

Step 2.2

Subtract $5$ from $23$ .

$\frac{96 x - 185}{15} = 2 x + 18$

Step 3

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

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Step 3.1

Subtract $2 x$ from both sides of the equation.

$\frac{96 x - 185}{15} - 2 x = 18$

Step 3.2

To write $- 2 x$ as a fraction with a common denominator, multiply by $\frac{15}{15}$ .

$\frac{96 x - 185}{15} - 2 x \cdot \frac{15}{15} = 18$

Step 3.3

Combine $- 2 x$ and $\frac{15}{15}$ .

$\frac{96 x - 185}{15} + \frac{- 2 x \cdot 15}{15} = 18$

Step 3.4

Combine the numerators over the common denominator.

$\frac{96 x - 185 - 2 x \cdot 15}{15} = 18$

Step 3.5

Simplify the numerator.

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Step 3.5.1

Multiply $15$ by $- 2$ .

$\frac{96 x - 185 - 30 x}{15} = 18$

Step 3.5.2

Subtract $30 x$ from $96 x$ .

$\frac{66 x - 185}{15} = 18$

Step 4

Multiply both sides by $15$ .

$\frac{66 x - 185}{15} \cdot 15 = 18 \cdot 15$

Step 5

Simplify.

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Step 5.1

Simplify the left side.

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Step 5.1.1

Cancel the common factor of $15$ .

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Step 5.1.1.1

Cancel the common factor.

$\frac{66 x - 185}{15} \cdot 15 = 18 \cdot 15$

Step 5.1.1.2

Rewrite the expression.

$66 x - 185 = 18 \cdot 15$

Step 5.2

Simplify the right side.

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Step 5.2.1

Multiply $18$ by $15$ .

$66 x - 185 = 270$

Step 6

Solve for $x$ .

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Step 6.1

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

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Step 6.1.1

Add $185$ to both sides of the equation.

$66 x = 270 + 185$

Step 6.1.2

Add $270$ and $185$ .

$66 x = 455$

Step 6.2

Divide each term in $66 x = 455$ by $66$ and simplify.

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Step 6.2.1

Divide each term in $66 x = 455$ by $66$ .

$\frac{66 x}{66} = \frac{455}{66}$

Step 6.2.2

Simplify the left side.

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Step 6.2.2.1

Cancel the common factor of $66$ .

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Step 6.2.2.1.1

Cancel the common factor.

$\frac{66 x}{66} = \frac{455}{66}$

Step 6.2.2.1.2

Divide $x$ by $1$ .

$x = \frac{455}{66}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$x = \frac{455}{66}$

Decimal Form:

$x = 6.8\overline{93}$

Mixed Number Form:

$x = 6 \frac{59}{66}$