Algebra Examples

$x + 5 = \frac{3 x + 13}{2}$

Step 1

Multiply both sides by $2$ .

$(x + 5) \cdot 2 = \frac{3 x + 13}{2} \cdot 2$

Step 2

Simplify.

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Step 2.1

Simplify the left side.

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Step 2.1.1

Simplify $(x + 5) \cdot 2$ .

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Step 2.1.1.1

Apply the distributive property.

$x \cdot 2 + 5 \cdot 2 = \frac{3 x + 13}{2} \cdot 2$

Step 2.1.1.2

Simplify the expression.

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Step 2.1.1.2.1

Move $2$ to the left of $x$ .

$2 \cdot x + 5 \cdot 2 = \frac{3 x + 13}{2} \cdot 2$

Step 2.1.1.2.2

Multiply $5$ by $2$ .

$2 x + 10 = \frac{3 x + 13}{2} \cdot 2$

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.

$2 x + 10 = \frac{3 x + 13}{2} \cdot 2$

Step 2.2.1.2

Rewrite the expression.

$2 x + 10 = 3 x + 13$

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 $3 x$ from both sides of the equation.

$2 x + 10 - 3 x = 13$

Step 3.1.2

Subtract $3 x$ from $2 x$ .

$- x + 10 = 13$

Step 3.2

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

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Step 3.2.1

Subtract $10$ from both sides of the equation.

$- x = 13 - 10$

Step 3.2.2

Subtract $10$ from $13$ .

$- x = 3$

Step 3.3

Divide each term in $- x = 3$ by $- 1$ and simplify.

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Step 3.3.1

Divide each term in $- x = 3$ by $- 1$ .

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

Step 3.3.2

Simplify the left side.

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Step 3.3.2.1

Dividing two negative values results in a positive value.

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

Step 3.3.2.2

Divide $x$ by $1$ .

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

Step 3.3.3

Simplify the right side.

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Step 3.3.3.1

Divide $3$ by $- 1$ .

$x = - 3$