Algebra Examples

$1 + \frac{x + 1}{3} = x - \frac{3 x + 1}{8}$

Step 1

Since $x$ is on the right side of the equation, switch the sides so it is on the left side of the equation.

$x - \frac{3 x + 1}{8} = 1 + \frac{x + 1}{3}$

Step 2

Simplify $x - \frac{3 x + 1}{8}$ .

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Step 2.1

To write $x$ as a fraction with a common denominator, multiply by $\frac{8}{8}$ .

$x \cdot \frac{8}{8} - \frac{3 x + 1}{8} = 1 + \frac{x + 1}{3}$

Step 2.2

Simplify terms.

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Step 2.2.1

Combine $x$ and $\frac{8}{8}$ .

$\frac{x \cdot 8}{8} - \frac{3 x + 1}{8} = 1 + \frac{x + 1}{3}$

Step 2.2.2

Combine the numerators over the common denominator.

$\frac{x \cdot 8 - (3 x + 1)}{8} = 1 + \frac{x + 1}{3}$

Step 2.3

Simplify the numerator.

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Step 2.3.1

Move $8$ to the left of $x$ .

$\frac{8 \cdot x - (3 x + 1)}{8} = 1 + \frac{x + 1}{3}$

Step 2.3.2

Apply the distributive property.

$\frac{8 x - (3 x) - 1 \cdot 1}{8} = 1 + \frac{x + 1}{3}$

Step 2.3.3

Multiply $3$ by $- 1$ .

$\frac{8 x - 3 x - 1 \cdot 1}{8} = 1 + \frac{x + 1}{3}$

Step 2.3.4

Multiply $- 1$ by $1$ .

$\frac{8 x - 3 x - 1}{8} = 1 + \frac{x + 1}{3}$

Step 2.3.5

Subtract $3 x$ from $8 x$ .

$\frac{5 x - 1}{8} = 1 + \frac{x + 1}{3}$

Step 3

Simplify $1 + \frac{x + 1}{3}$ .

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Step 3.1

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

$\frac{5 x - 1}{8} = \frac{3}{3} + \frac{x + 1}{3}$

Step 3.2

Combine the numerators over the common denominator.

$\frac{5 x - 1}{8} = \frac{3 + x + 1}{3}$

Step 3.3

Add $3$ and $1$ .

$\frac{5 x - 1}{8} = \frac{x + 4}{3}$

Step 4

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

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Step 4.1

Subtract $\frac{x + 4}{3}$ from both sides of the equation.

$\frac{5 x - 1}{8} - \frac{x + 4}{3} = 0$

Step 4.2

To write $\frac{5 x - 1}{8}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$\frac{5 x - 1}{8} \cdot \frac{3}{3} - \frac{x + 4}{3} = 0$

Step 4.3

To write $- \frac{x + 4}{3}$ as a fraction with a common denominator, multiply by $\frac{8}{8}$ .

$\frac{5 x - 1}{8} \cdot \frac{3}{3} - \frac{x + 4}{3} \cdot \frac{8}{8} = 0$

Step 4.4

Write each expression with a common denominator of $24$ , by multiplying each by an appropriate factor of $1$ .

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Step 4.4.1

Multiply $\frac{5 x - 1}{8}$ by $\frac{3}{3}$ .

$\frac{(5 x - 1) \cdot 3}{8 \cdot 3} - \frac{x + 4}{3} \cdot \frac{8}{8} = 0$

Step 4.4.2

Multiply $8$ by $3$ .

$\frac{(5 x - 1) \cdot 3}{24} - \frac{x + 4}{3} \cdot \frac{8}{8} = 0$

Step 4.4.3

Multiply $\frac{x + 4}{3}$ by $\frac{8}{8}$ .

$\frac{(5 x - 1) \cdot 3}{24} - \frac{(x + 4) \cdot 8}{3 \cdot 8} = 0$

Step 4.4.4

Multiply $3$ by $8$ .

$\frac{(5 x - 1) \cdot 3}{24} - \frac{(x + 4) \cdot 8}{24} = 0$

Step 4.5

Combine the numerators over the common denominator.

$\frac{(5 x - 1) \cdot 3 - (x + 4) \cdot 8}{24} = 0$

Step 4.6

Simplify the numerator.

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Step 4.6.1

Apply the distributive property.

$\frac{5 x \cdot 3 - 1 \cdot 3 - (x + 4) \cdot 8}{24} = 0$

Step 4.6.2

Multiply $3$ by $5$ .

$\frac{15 x - 1 \cdot 3 - (x + 4) \cdot 8}{24} = 0$

Step 4.6.3

Multiply $- 1$ by $3$ .

$\frac{15 x - 3 - (x + 4) \cdot 8}{24} = 0$

Step 4.6.4

Apply the distributive property.

$\frac{15 x - 3 + (- x - 1 \cdot 4) \cdot 8}{24} = 0$

Step 4.6.5

Multiply $- 1$ by $4$ .

$\frac{15 x - 3 + (- x - 4) \cdot 8}{24} = 0$

Step 4.6.6

Apply the distributive property.

$\frac{15 x - 3 - x \cdot 8 - 4 \cdot 8}{24} = 0$

Step 4.6.7

Multiply $8$ by $- 1$ .

$\frac{15 x - 3 - 8 x - 4 \cdot 8}{24} = 0$

Step 4.6.8

Multiply $- 4$ by $8$ .

$\frac{15 x - 3 - 8 x - 32}{24} = 0$

Step 4.6.9

Subtract $8 x$ from $15 x$ .

$\frac{7 x - 3 - 32}{24} = 0$

Step 4.6.10

Subtract $32$ from $- 3$ .

$\frac{7 x - 35}{24} = 0$

Step 4.6.11

Factor $7$ out of $7 x - 35$ .

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Step 4.6.11.1

Factor $7$ out of $7 x$ .

$\frac{7 (x) - 35}{24} = 0$

Step 4.6.11.2

Factor $7$ out of $- 35$ .

$\frac{7 x + 7 \cdot - 5}{24} = 0$

Step 4.6.11.3

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

$\frac{7 (x - 5)}{24} = 0$

Step 5

Set the numerator equal to zero.

$7 (x - 5) = 0$

Step 6

Solve the equation for $x$ .

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Step 6.1

Divide each term in $7 (x - 5) = 0$ by $7$ and simplify.

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Step 6.1.1

Divide each term in $7 (x - 5) = 0$ by $7$ .

$\frac{7 (x - 5)}{7} = \frac{0}{7}$

Step 6.1.2

Simplify the left side.

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Step 6.1.2.1

Cancel the common factor of $7$ .

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Step 6.1.2.1.1

Cancel the common factor.

$\frac{7 (x - 5)}{7} = \frac{0}{7}$

Step 6.1.2.1.2

Divide $x - 5$ by $1$ .

$x - 5 = \frac{0}{7}$

Step 6.1.3

Simplify the right side.

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Step 6.1.3.1

Divide $0$ by $7$ .

$x - 5 = 0$

Step 6.2

Add $5$ to both sides of the equation.

$x = 5$