Pre-Algebra Examples

$- 6 (x + 1) + 8 x = 2 (x - 3)$

Step 1

Simplify $- 6 (x + 1) + 8 x$ .

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Step 1.1

Simplify each term.

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Step 1.1.1

Apply the distributive property.

$- 6 x - 6 \cdot 1 + 8 x = 2 (x - 3)$

Step 1.1.2

Multiply $- 6$ by $1$ .

$- 6 x - 6 + 8 x = 2 (x - 3)$

Step 1.2

Add $- 6 x$ and $8 x$ .

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

Step 2

Simplify $2 (x - 3)$ .

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Step 2.1

Apply the distributive property.

$2 x - 6 = 2 x + 2 \cdot - 3$

Step 2.2

Multiply $2$ by $- 3$ .

$2 x - 6 = 2 x - 6$

Step 3

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

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Step 3.1

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

$2 x - 6 - 2 x = - 6$

Step 3.2

Combine the opposite terms in $2 x - 6 - 2 x$ .

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Step 3.2.1

Subtract $2 x$ from $2 x$ .

$0 - 6 = - 6$

Step 3.2.2

Subtract $6$ from $0$ .

$- 6 = - 6$

Step 4

Since $- 6 = - 6$ , 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:

$(- \infty, \infty)$