Pre-Algebra Examples

$12 (x + 3) = 4 (2 x + 9) + 4 x$

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.

$4 (2 x + 9) + 4 x = 12 (x + 3)$

Step 2

Simplify $4 (2 x + 9) + 4 x$ .

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Step 2.1

Simplify each term.

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Step 2.1.1

Apply the distributive property.

$4 (2 x) + 4 \cdot 9 + 4 x = 12 (x + 3)$

Step 2.1.2

Multiply $2$ by $4$ .

$8 x + 4 \cdot 9 + 4 x = 12 (x + 3)$

Step 2.1.3

Multiply $4$ by $9$ .

$8 x + 36 + 4 x = 12 (x + 3)$

Step 2.2

Add $8 x$ and $4 x$ .

$12 x + 36 = 12 (x + 3)$

Step 3

Simplify $12 (x + 3)$ .

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Step 3.1

Apply the distributive property.

$12 x + 36 = 12 x + 12 \cdot 3$

Step 3.2

Multiply $12$ by $3$ .

$12 x + 36 = 12 x + 36$

Step 4

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

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Step 4.1

Subtract $12 x$ from both sides of the equation.

$12 x + 36 - 12 x = 36$

Step 4.2

Combine the opposite terms in $12 x + 36 - 12 x$ .

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Step 4.2.1

Subtract $12 x$ from $12 x$ .

$0 + 36 = 36$

Step 4.2.2

Add $0$ and $36$ .

$36 = 36$

Step 5

Since $36 = 36$ , 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:

$(- \infty, \infty)$