Algebra Examples

$2 (8 x - 4) - 2 x \leq 14 x + 12$

Step 1

Simplify $2 (8 x - 4) - 2 x$ .

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Step 1.1

Simplify each term.

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Step 1.1.1

Apply the distributive property.

$2 (8 x) + 2 \cdot - 4 - 2 x \leq 14 x + 12$

Step 1.1.2

Multiply $8$ by $2$ .

$16 x + 2 \cdot - 4 - 2 x \leq 14 x + 12$

Step 1.1.3

Multiply $2$ by $- 4$ .

$16 x - 8 - 2 x \leq 14 x + 12$

Step 1.2

Subtract $2 x$ from $16 x$ .

$14 x - 8 \leq 14 x + 12$

Step 2

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

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Step 2.1

Subtract $14 x$ from both sides of the inequality.

$14 x - 8 - 14 x \leq 12$

Step 2.2

Combine the opposite terms in $14 x - 8 - 14 x$ .

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Step 2.2.1

Subtract $14 x$ from $14 x$ .

$0 - 8 \leq 12$

Step 2.2.2

Subtract $8$ from $0$ .

$- 8 \leq 12$

Step 3

Since $- 8 \leq 12$ , the inequality will always be true for any value of $x$ .

All real numbers

Step 4

The result can be shown in multiple forms.

All real numbers

Interval Notation:

$(- \infty, \infty)$