Pre-Algebra Examples

$8 = \frac{3 x + 1}{2}$

Step 1

Rewrite the equation as $\frac{3 x + 1}{2} = 8$ .

$\frac{3 x + 1}{2} = 8$

Step 2

Multiply both sides by $2$ .

$\frac{3 x + 1}{2} \cdot 2 = 8 \cdot 2$

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 $2$ .

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Step 3.1.1.1

Cancel the common factor.

$\frac{3 x + 1}{2} \cdot 2 = 8 \cdot 2$

Step 3.1.1.2

Rewrite the expression.

$3 x + 1 = 8 \cdot 2$

Step 3.2

Simplify the right side.

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Step 3.2.1

Multiply $8$ by $2$ .

$3 x + 1 = 16$

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 $1$ from both sides of the equation.

$3 x = 16 - 1$

Step 4.1.2

Subtract $1$ from $16$ .

$3 x = 15$

Step 4.2

Divide each term in $3 x = 15$ by $3$ and simplify.

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Step 4.2.1

Divide each term in $3 x = 15$ by $3$ .

$\frac{3 x}{3} = \frac{15}{3}$

Step 4.2.2

Simplify the left side.

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Step 4.2.2.1

Cancel the common factor of $3$ .

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Step 4.2.2.1.1

Cancel the common factor.

$\frac{3 x}{3} = \frac{15}{3}$

Step 4.2.2.1.2

Divide $x$ by $1$ .

$x = \frac{15}{3}$

Step 4.2.3

Simplify the right side.

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Step 4.2.3.1

Divide $15$ by $3$ .

$x = 5$