Finite Math Examples

$8 (6 x - 2) - 12 x < 6 (1 + 6 x) - 4$

Step 1

Simplify $8 (6 x - 2) - 12 x$ .

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Step 1.1

Simplify each term.

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Step 1.1.1

Apply the distributive property.

$8 (6 x) + 8 \cdot - 2 - 12 x < 6 (1 + 6 x) - 4$

Step 1.1.2

Multiply $6$ by $8$ .

$48 x + 8 \cdot - 2 - 12 x < 6 (1 + 6 x) - 4$

Step 1.1.3

Multiply $8$ by $- 2$ .

$48 x - 16 - 12 x < 6 (1 + 6 x) - 4$

Step 1.2

Subtract $12 x$ from $48 x$ .

$36 x - 16 < 6 (1 + 6 x) - 4$

Step 2

Simplify $6 (1 + 6 x) - 4$ .

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Step 2.1

Simplify each term.

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Step 2.1.1

Apply the distributive property.

$36 x - 16 < 6 \cdot 1 + 6 (6 x) - 4$

Step 2.1.2

Multiply $6$ by $1$ .

$36 x - 16 < 6 + 6 (6 x) - 4$

Step 2.1.3

Multiply $6$ by $6$ .

$36 x - 16 < 6 + 36 x - 4$

Step 2.2

Subtract $4$ from $6$ .

$36 x - 16 < 36 x + 2$

Step 3

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

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Step 3.1

Subtract $36 x$ from both sides of the inequality.

$36 x - 16 - 36 x < 2$

Step 3.2

Combine the opposite terms in $36 x - 16 - 36 x$ .

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Step 3.2.1

Subtract $36 x$ from $36 x$ .

$0 - 16 < 2$

Step 3.2.2

Subtract $16$ from $0$ .

$- 16 < 2$

Step 4

Since $- 16 < 2$ , the inequality 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:

$(- \infty, \infty)$