Algebra Examples

$4 x + \frac{x + 3}{6} = 13$

Step 1

Simplify $4 x + \frac{x + 3}{6}$ .

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Step 1.1

To write $4 x$ as a fraction with a common denominator, multiply by $\frac{6}{6}$ .

$4 x \cdot \frac{6}{6} + \frac{x + 3}{6} = 13$

Step 1.2

Simplify terms.

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Step 1.2.1

Combine $4 x$ and $\frac{6}{6}$ .

$\frac{4 x \cdot 6}{6} + \frac{x + 3}{6} = 13$

Step 1.2.2

Combine the numerators over the common denominator.

$\frac{4 x \cdot 6 + x + 3}{6} = 13$

Step 1.3

Simplify the numerator.

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Step 1.3.1

Multiply $6$ by $4$ .

$\frac{24 x + x + 3}{6} = 13$

Step 1.3.2

Add $24 x$ and $x$ .

$\frac{25 x + 3}{6} = 13$

Step 2

Multiply both sides by $6$ .

$\frac{25 x + 3}{6} \cdot 6 = 13 \cdot 6$

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 $6$ .

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Step 3.1.1.1

Cancel the common factor.

$\frac{25 x + 3}{6} \cdot 6 = 13 \cdot 6$

Step 3.1.1.2

Rewrite the expression.

$25 x + 3 = 13 \cdot 6$

Step 3.2

Simplify the right side.

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Step 3.2.1

Multiply $13$ by $6$ .

$25 x + 3 = 78$

Step 4

Solve for $x$ .

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Step 4.1

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

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Step 4.1.1

Subtract $3$ from both sides of the equation.

$25 x = 78 - 3$

Step 4.1.2

Subtract $3$ from $78$ .

$25 x = 75$

Step 4.2

Divide each term in $25 x = 75$ by $25$ and simplify.

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Step 4.2.1

Divide each term in $25 x = 75$ by $25$ .

$\frac{25 x}{25} = \frac{75}{25}$

Step 4.2.2

Simplify the left side.

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Step 4.2.2.1

Cancel the common factor of $25$ .

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Step 4.2.2.1.1

Cancel the common factor.

$\frac{25 x}{25} = \frac{75}{25}$

Step 4.2.2.1.2

Divide $x$ by $1$ .

$x = \frac{75}{25}$

Step 4.2.3

Simplify the right side.

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Step 4.2.3.1

Divide $75$ by $25$ .

$x = 3$