Algebra Examples

$2 - \frac{3 x - 7}{4} + \frac{x + 17}{5} = 0$

Step 1

Simplify $2 - \frac{3 x - 7}{4} + \frac{x + 17}{5}$ .

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Step 1.1

Find the common denominator.

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Step 1.1.1

Write $2$ as a fraction with denominator $1$ .

$\frac{2}{1} - \frac{3 x - 7}{4} + \frac{x + 17}{5} = 0$

Step 1.1.2

Multiply $\frac{2}{1}$ by $\frac{20}{20}$ .

$\frac{2}{1} \cdot \frac{20}{20} - \frac{3 x - 7}{4} + \frac{x + 17}{5} = 0$

Step 1.1.3

Multiply $\frac{2}{1}$ by $\frac{20}{20}$ .

$\frac{2 \cdot 20}{20} - \frac{3 x - 7}{4} + \frac{x + 17}{5} = 0$

Step 1.1.4

Multiply $\frac{3 x - 7}{4}$ by $\frac{5}{5}$ .

$\frac{2 \cdot 20}{20} - (\frac{3 x - 7}{4} \cdot \frac{5}{5}) + \frac{x + 17}{5} = 0$

Step 1.1.5

Multiply $\frac{3 x - 7}{4}$ by $\frac{5}{5}$ .

$\frac{2 \cdot 20}{20} - \frac{(3 x - 7) \cdot 5}{4 \cdot 5} + \frac{x + 17}{5} = 0$

Step 1.1.6

Multiply $\frac{x + 17}{5}$ by $\frac{4}{4}$ .

$\frac{2 \cdot 20}{20} - \frac{(3 x - 7) \cdot 5}{4 \cdot 5} + \frac{x + 17}{5} \cdot \frac{4}{4} = 0$

Step 1.1.7

Multiply $\frac{x + 17}{5}$ by $\frac{4}{4}$ .

$\frac{2 \cdot 20}{20} - \frac{(3 x - 7) \cdot 5}{4 \cdot 5} + \frac{(x + 17) \cdot 4}{5 \cdot 4} = 0$

Step 1.1.8

Multiply $4$ by $5$ .

$\frac{2 \cdot 20}{20} - \frac{(3 x - 7) \cdot 5}{20} + \frac{(x + 17) \cdot 4}{5 \cdot 4} = 0$

Step 1.1.9

Reorder the factors of $5 \cdot 4$ .

$\frac{2 \cdot 20}{20} - \frac{(3 x - 7) \cdot 5}{20} + \frac{(x + 17) \cdot 4}{4 \cdot 5} = 0$

Step 1.1.10

Multiply $4$ by $5$ .

$\frac{2 \cdot 20}{20} - \frac{(3 x - 7) \cdot 5}{20} + \frac{(x + 17) \cdot 4}{20} = 0$

Step 1.2

Combine the numerators over the common denominator.

$\frac{2 \cdot 20 - (3 x - 7) \cdot 5 + (x + 17) \cdot 4}{20} = 0$

Step 1.3

Simplify each term.

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Step 1.3.1

Multiply $2$ by $20$ .

$\frac{40 - (3 x - 7) \cdot 5 + (x + 17) \cdot 4}{20} = 0$

Step 1.3.2

Apply the distributive property.

$\frac{40 + (- (3 x) - - 7) \cdot 5 + (x + 17) \cdot 4}{20} = 0$

Step 1.3.3

Multiply $3$ by $- 1$ .

$\frac{40 + (- 3 x - - 7) \cdot 5 + (x + 17) \cdot 4}{20} = 0$

Step 1.3.4

Multiply $- 1$ by $- 7$ .

$\frac{40 + (- 3 x + 7) \cdot 5 + (x + 17) \cdot 4}{20} = 0$

Step 1.3.5

Apply the distributive property.

$\frac{40 - 3 x \cdot 5 + 7 \cdot 5 + (x + 17) \cdot 4}{20} = 0$

Step 1.3.6

Multiply $5$ by $- 3$ .

$\frac{40 - 15 x + 7 \cdot 5 + (x + 17) \cdot 4}{20} = 0$

Step 1.3.7

Multiply $7$ by $5$ .

$\frac{40 - 15 x + 35 + (x + 17) \cdot 4}{20} = 0$

Step 1.3.8

Apply the distributive property.

$\frac{40 - 15 x + 35 + x \cdot 4 + 17 \cdot 4}{20} = 0$

Step 1.3.9

Move $4$ to the left of $x$ .

$\frac{40 - 15 x + 35 + 4 \cdot x + 17 \cdot 4}{20} = 0$

Step 1.3.10

Multiply $17$ by $4$ .

$\frac{40 - 15 x + 35 + 4 x + 68}{20} = 0$

Step 1.4

Simplify terms.

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Step 1.4.1

Add $40$ and $35$ .

$\frac{- 15 x + 75 + 4 x + 68}{20} = 0$

Step 1.4.2

Add $- 15 x$ and $4 x$ .

$\frac{- 11 x + 75 + 68}{20} = 0$

Step 1.4.3

Add $75$ and $68$ .

$\frac{- 11 x + 143}{20} = 0$

Step 1.4.4

Factor $11$ out of $- 11 x + 143$ .

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Step 1.4.4.1

Factor $11$ out of $- 11 x$ .

$\frac{11 (- x) + 143}{20} = 0$

Step 1.4.4.2

Factor $11$ out of $143$ .

$\frac{11 (- x) + 11 (13)}{20} = 0$

Step 1.4.4.3

Factor $11$ out of $11 (- x) + 11 (13)$ .

$\frac{11 (- x + 13)}{20} = 0$

Step 1.4.5

Factor $- 1$ out of $- x$ .

$\frac{11 (- (x) + 13)}{20} = 0$

Step 1.4.6

Rewrite $13$ as $- 1 (- 13)$ .

$\frac{11 (- (x) - 1 (- 13))}{20} = 0$

Step 1.4.7

Factor $- 1$ out of $- (x) - 1 (- 13)$ .

$\frac{11 (- (x - 13))}{20} = 0$

Step 1.4.8

Simplify the expression.

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Step 1.4.8.1

Rewrite $- (x - 13)$ as $- 1 (x - 13)$ .

$\frac{11 (- 1 (x - 13))}{20} = 0$

Step 1.4.8.2

Move the negative in front of the fraction.

$- \frac{11 (x - 13)}{20} = 0$

Step 2

Set the numerator equal to zero.

$11 (x - 13) = 0$

Step 3

Solve the equation for $x$ .

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Step 3.1

Divide each term in $11 (x - 13) = 0$ by $11$ and simplify.

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Step 3.1.1

Divide each term in $11 (x - 13) = 0$ by $11$ .

$\frac{11 (x - 13)}{11} = \frac{0}{11}$

Step 3.1.2

Simplify the left side.

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Step 3.1.2.1

Cancel the common factor of $11$ .

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Step 3.1.2.1.1

Cancel the common factor.

$\frac{11 (x - 13)}{11} = \frac{0}{11}$

Step 3.1.2.1.2

Divide $x - 13$ by $1$ .

$x - 13 = \frac{0}{11}$

Step 3.1.3

Simplify the right side.

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Step 3.1.3.1

Divide $0$ by $11$ .

$x - 13 = 0$

Step 3.2

Add $13$ to both sides of the equation.

$x = 13$