Precalculus Examples

$- 7 + 8 b \geq 4 (2 b - 3)$

Step 1

Simplify $4 (2 b - 3)$ .

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Step 1.1

Rewrite.

$- 7 + 8 b \geq 0 + 0 + 4 (2 b - 3)$

Step 1.2

Simplify by adding zeros.

$- 7 + 8 b \geq 4 (2 b - 3)$

Step 1.3

Apply the distributive property.

$- 7 + 8 b \geq 4 (2 b) + 4 \cdot - 3$

Step 1.4

Multiply.

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Step 1.4.1

Multiply $2$ by $4$ .

$- 7 + 8 b \geq 8 b + 4 \cdot - 3$

Step 1.4.2

Multiply $4$ by $- 3$ .

$- 7 + 8 b \geq 8 b - 12$

Step 2

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

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Step 2.1

Subtract $8 b$ from both sides of the inequality.

$- 7 + 8 b - 8 b \geq - 12$

Step 2.2

Combine the opposite terms in $- 7 + 8 b - 8 b$ .

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Step 2.2.1

Subtract $8 b$ from $8 b$ .

$- 7 + 0 \geq - 12$

Step 2.2.2

Add $- 7$ and $0$ .

$- 7 \geq - 12$

Step 3

Since $- 7 \geq - 12$ , the inequality will always be true for any value of $b$ .

All real numbers

Step 4

The result can be shown in multiple forms.

All real numbers

Interval Notation:

$(- \infty, \infty)$