Pre-Algebra Examples

$8 (c - 9) = 6 (2 c - 12) - 4 c$

Step 1

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

$6 (2 c - 12) - 4 c = 8 (c - 9)$

Step 2

Simplify $6 (2 c - 12) - 4 c$ .

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Step 2.1

Simplify each term.

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Step 2.1.1

Apply the distributive property.

$6 (2 c) + 6 \cdot - 12 - 4 c = 8 (c - 9)$

Step 2.1.2

Multiply $2$ by $6$ .

$12 c + 6 \cdot - 12 - 4 c = 8 (c - 9)$

Step 2.1.3

Multiply $6$ by $- 12$ .

$12 c - 72 - 4 c = 8 (c - 9)$

Step 2.2

Subtract $4 c$ from $12 c$ .

$8 c - 72 = 8 (c - 9)$

Step 3

Simplify $8 (c - 9)$ .

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Step 3.1

Apply the distributive property.

$8 c - 72 = 8 c + 8 \cdot - 9$

Step 3.2

Multiply $8$ by $- 9$ .

$8 c - 72 = 8 c - 72$

Step 4

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

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Step 4.1

Subtract $8 c$ from both sides of the equation.

$8 c - 72 - 8 c = - 72$

Step 4.2

Combine the opposite terms in $8 c - 72 - 8 c$ .

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Step 4.2.1

Subtract $8 c$ from $8 c$ .

$0 - 72 = - 72$

Step 4.2.2

Subtract $72$ from $0$ .

$- 72 = - 72$

Step 5

Since $- 72 = - 72$ , the equation will always be true for any value of $c$ .

All real numbers

Step 6

The result can be shown in multiple forms.

All real numbers

Interval Notation:

$(- \infty, \infty)$