Pre-Algebra Examples

$\frac{3 x + 15}{2} = 20$

Step 1

Multiply both sides by $2$ .

$\frac{3 x + 15}{2} \cdot 2 = 20 \cdot 2$

Step 2

Simplify.

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Step 2.1

Simplify the left side.

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Step 2.1.1

Simplify $\frac{3 x + 15}{2} \cdot 2$ .

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Step 2.1.1.1

Factor $3$ out of $3 x + 15$ .

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Step 2.1.1.1.1

Factor $3$ out of $3 x$ .

$\frac{3 (x) + 15}{2} \cdot 2 = 20 \cdot 2$

Step 2.1.1.1.2

Factor $3$ out of $15$ .

$\frac{3 x + 3 \cdot 5}{2} \cdot 2 = 20 \cdot 2$

Step 2.1.1.1.3

Factor $3$ out of $3 x + 3 \cdot 5$ .

$\frac{3 (x + 5)}{2} \cdot 2 = 20 \cdot 2$

$\frac{3 (x + 5)}{2} \cdot 2 = 20 \cdot 2$

Step 2.1.1.2

Cancel the common factor of $2$ .

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Step 2.1.1.2.1

Cancel the common factor.

$\frac{3 (x + 5)}{2} \cdot 2 = 20 \cdot 2$

Step 2.1.1.2.2

Rewrite the expression.

$3 (x + 5) = 20 \cdot 2$

$3 (x + 5) = 20 \cdot 2$

Step 2.1.1.3

Apply the distributive property.

$3 x + 3 \cdot 5 = 20 \cdot 2$

Step 2.1.1.4

Multiply $3$ by $5$ .

$3 x + 15 = 20 \cdot 2$

$3 x + 15 = 20 \cdot 2$

$3 x + 15 = 20 \cdot 2$

Step 2.2

Simplify the right side.

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Step 2.2.1

Multiply $20$ by $2$ .

$3 x + 15 = 40$

$3 x + 15 = 40$

$3 x + 15 = 40$

Step 3

Solve for $x$ .

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Step 3.1

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

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Step 3.1.1

Subtract $15$ from both sides of the equation.

$3 x = 40 - 15$

Step 3.1.2

Subtract $15$ from $40$ .

$3 x = 25$

$3 x = 25$

Step 3.2

Divide each term in $3 x = 25$ by $3$ and simplify.

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Step 3.2.1

Divide each term in $3 x = 25$ by $3$ .

$\frac{3 x}{3} = \frac{25}{3}$

Step 3.2.2

Simplify the left side.

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Step 3.2.2.1

Cancel the common factor of $3$ .

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Step 3.2.2.1.1

Cancel the common factor.

$\frac{3 x}{3} = \frac{25}{3}$

Step 3.2.2.1.2

Divide $x$ by $1$ .

$x = \frac{25}{3}$

$x = \frac{25}{3}$

$x = \frac{25}{3}$

$x = \frac{25}{3}$

$x = \frac{25}{3}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$x = \frac{25}{3}$

Decimal Form:

$x = 8.\overline{3}$

Mixed Number Form:

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

$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$