Algebra Examples

$4 (\frac{1}{2} x + 3) = 3 x + 12 - x$

Step 1

Since $x$ is on the right side of the equation, switch the sides so it is on the left side of the equation.

$3 x + 12 - x = 4 (\frac{1}{2} x + 3)$

Step 2

Subtract $x$ from $3 x$ .

$2 x + 12 = 4 (\frac{1}{2} x + 3)$

Step 3

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

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Step 3.1

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

$2 x + 12 = 4 (\frac{x}{2} + 3)$

Step 3.2

Apply the distributive property.

$2 x + 12 = 4 \frac{x}{2} + 4 \cdot 3$

Step 3.3

Cancel the common factor of $2$ .

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Step 3.3.1

Factor $2$ out of $4$ .

$2 x + 12 = 2 (2) \frac{x}{2} + 4 \cdot 3$

Step 3.3.2

Cancel the common factor.

$2 x + 12 = 2 \cdot 2 \frac{x}{2} + 4 \cdot 3$

Step 3.3.3

Rewrite the expression.

$2 x + 12 = 2 x + 4 \cdot 3$

Step 3.4

Multiply $4$ by $3$ .

$2 x + 12 = 2 x + 12$

Step 4

Move all terms containing $x$ to the left side of the equation.

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Step 4.1

Subtract $2 x$ from both sides of the equation.

$2 x + 12 - 2 x = 12$

Step 4.2

Combine the opposite terms in $2 x + 12 - 2 x$ .

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Step 4.2.1

Subtract $2 x$ from $2 x$ .

$0 + 12 = 12$

Step 4.2.2

Add $0$ and $12$ .

$12 = 12$

Step 5

Since $12 = 12$ , the equation will always be true for any value of $x$ .

All real numbers

Step 6

The result can be shown in multiple forms.

All real numbers

Interval Notation:

$(- \infty, \infty)$