Algebra Examples

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

Step 1

Solve $- 18 < 2$ .

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Step 1.1

Simplify $6 (2 x - 3) - 8 x$ .

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Step 1.1.1

Simplify each term.

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Step 1.1.1.1

Apply the distributive property.

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

Step 1.1.1.2

Multiply $2$ by $6$ .

$12 x + 6 \cdot - 3 - 8 x < 2 (2 + 2 x) - 2$

Step 1.1.1.3

Multiply $6$ by $- 3$ .

$12 x - 18 - 8 x < 2 (2 + 2 x) - 2$

Step 1.1.2

Subtract $8 x$ from $12 x$ .

$4 x - 18 < 2 (2 + 2 x) - 2$

Step 1.2

Simplify $2 (2 + 2 x) - 2$ .

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Step 1.2.1

Simplify each term.

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Step 1.2.1.1

Apply the distributive property.

$4 x - 18 < 2 \cdot 2 + 2 (2 x) - 2$

Step 1.2.1.2

Multiply $2$ by $2$ .

$4 x - 18 < 4 + 2 (2 x) - 2$

Step 1.2.1.3

Multiply $2$ by $2$ .

$4 x - 18 < 4 + 4 x - 2$

Step 1.2.2

Subtract $2$ from $4$ .

$4 x - 18 < 4 x + 2$

Step 1.3

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

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Step 1.3.1

Subtract $4 x$ from both sides of the inequality.

$4 x - 18 - 4 x < 2$

Step 1.3.2

Combine the opposite terms in $4 x - 18 - 4 x$ .

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Step 1.3.2.1

Subtract $4 x$ from $4 x$ .

$0 - 18 < 2$

Step 1.3.2.2

Subtract $18$ from $0$ .

$- 18 < 2$

Step 1.4

Since $- 18 < 2$ , the inequality will always be true.

Always true

Step 2

Use the inequality Always true to build the set notation.

${x | A l w a y s (t r u e)}$