Algebra Examples

$4 = \frac{1}{2} (3 X + 4)$

Step 1

Rewrite the equation as $\frac{1}{2} \cdot (3 X + 4) = 4$ .

$\frac{1}{2} \cdot (3 X + 4) = 4$

Step 2

Multiply both sides of the equation by $2$ .

$2 (\frac{1}{2} \cdot (3 X + 4)) = 2 \cdot 4$

Step 3

Simplify both sides of the equation.

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Step 3.1

Simplify the left side.

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Step 3.1.1

Simplify $2 (\frac{1}{2} \cdot (3 X + 4))$ .

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Step 3.1.1.1

Apply the distributive property.

$2 (\frac{1}{2} (3 X) + \frac{1}{2} \cdot 4) = 2 \cdot 4$

Step 3.1.1.2

Multiply $\frac{1}{2} (3 X)$ .

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Step 3.1.1.2.1

Combine $3$ and $\frac{1}{2}$ .

$2 (\frac{3}{2} X + \frac{1}{2} \cdot 4) = 2 \cdot 4$

Step 3.1.1.2.2

Combine $\frac{3}{2}$ and $X$ .

$2 (\frac{3 X}{2} + \frac{1}{2} \cdot 4) = 2 \cdot 4$

Step 3.1.1.3

Cancel the common factor of $2$ .

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Step 3.1.1.3.1

Factor $2$ out of $4$ .

$2 (\frac{3 X}{2} + \frac{1}{2} \cdot (2 (2))) = 2 \cdot 4$

Step 3.1.1.3.2

Cancel the common factor.

$2 (\frac{3 X}{2} + \frac{1}{2} \cdot (2 \cdot 2)) = 2 \cdot 4$

Step 3.1.1.3.3

Rewrite the expression.

$2 (\frac{3 X}{2} + 2) = 2 \cdot 4$

Step 3.1.1.4

Apply the distributive property.

$2 \frac{3 X}{2} + 2 \cdot 2 = 2 \cdot 4$

Step 3.1.1.5

Cancel the common factor of $2$ .

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Step 3.1.1.5.1

Cancel the common factor.

$2 \frac{3 X}{2} + 2 \cdot 2 = 2 \cdot 4$

Step 3.1.1.5.2

Rewrite the expression.

$3 X + 2 \cdot 2 = 2 \cdot 4$

Step 3.1.1.6

Multiply $2$ by $2$ .

$3 X + 4 = 2 \cdot 4$

Step 3.2

Simplify the right side.

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Step 3.2.1

Multiply $2$ by $4$ .

$3 X + 4 = 8$

Step 4

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

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Step 4.1

Subtract $4$ from both sides of the equation.

$3 X = 8 - 4$

Step 4.2

Subtract $4$ from $8$ .

$3 X = 4$

Step 5

Divide each term in $3 X = 4$ by $3$ and simplify.

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Step 5.1

Divide each term in $3 X = 4$ by $3$ .

$\frac{3 X}{3} = \frac{4}{3}$

Step 5.2

Simplify the left side.

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Step 5.2.1

Cancel the common factor of $3$ .

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Step 5.2.1.1

Cancel the common factor.

$\frac{3 X}{3} = \frac{4}{3}$

Step 5.2.1.2

Divide $X$ by $1$ .

$X = \frac{4}{3}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$X = \frac{4}{3}$

Decimal Form:

$X = 1.\overline{3}$

Mixed Number Form:

$X = 1 \frac{1}{3}$