Pre-Algebra Examples

$3 (6 - 4 x) = - 2 (6 x - 9)$

Step 1

Simplify $3 (6 - 4 x)$ .

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Step 1.1

Rewrite.

$0 + 0 + 3 (6 - 4 x) = - 2 (6 x - 9)$

Step 1.2

Simplify by adding zeros.

$3 (6 - 4 x) = - 2 (6 x - 9)$

Step 1.3

Apply the distributive property.

$3 \cdot 6 + 3 (- 4 x) = - 2 (6 x - 9)$

Step 1.4

Multiply.

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Step 1.4.1

Multiply $3$ by $6$ .

$18 + 3 (- 4 x) = - 2 (6 x - 9)$

Step 1.4.2

Multiply $- 4$ by $3$ .

$18 - 12 x = - 2 (6 x - 9)$

Step 2

Simplify $- 2 (6 x - 9)$ .

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Step 2.1

Apply the distributive property.

$18 - 12 x = - 2 (6 x) - 2 \cdot - 9$

Step 2.2

Multiply.

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Step 2.2.1

Multiply $6$ by $- 2$ .

$18 - 12 x = - 12 x - 2 \cdot - 9$

Step 2.2.2

Multiply $- 2$ by $- 9$ .

$18 - 12 x = - 12 x + 18$

Step 3

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

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Step 3.1

Add $12 x$ to both sides of the equation.

$18 - 12 x + 12 x = 18$

Step 3.2

Combine the opposite terms in $18 - 12 x + 12 x$ .

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Step 3.2.1

Add $- 12 x$ and $12 x$ .

$18 + 0 = 18$

Step 3.2.2

Add $18$ and $0$ .

$18 = 18$

Step 4

Since $18 = 18$ , the equation will always be true for any value of $x$ .

All real numbers

Step 5

The result can be shown in multiple forms.

All real numbers

Interval Notation:

$(- \infty, \infty)$