Finite Math Examples

$8 (3 - 2 p) - 16 (1 - p) - 3 (p - 4) = 20 - 3 p$

Step 1

Simplify $8 (3 - 2 p) - 16 (1 - p) - 3 (p - 4)$ .

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Step 1.1

Simplify each term.

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Step 1.1.1

Apply the distributive property.

$8 \cdot 3 + 8 (- 2 p) - 16 (1 - p) - 3 (p - 4) = 20 - 3 p$

Step 1.1.2

Multiply $8$ by $3$ .

$24 + 8 (- 2 p) - 16 (1 - p) - 3 (p - 4) = 20 - 3 p$

Step 1.1.3

Multiply $- 2$ by $8$ .

$24 - 16 p - 16 (1 - p) - 3 (p - 4) = 20 - 3 p$

Step 1.1.4

Apply the distributive property.

$24 - 16 p - 16 \cdot 1 - 16 (- p) - 3 (p - 4) = 20 - 3 p$

Step 1.1.5

Multiply $- 16$ by $1$ .

$24 - 16 p - 16 - 16 (- p) - 3 (p - 4) = 20 - 3 p$

Step 1.1.6

Multiply $- 1$ by $- 16$ .

$24 - 16 p - 16 + 16 p - 3 (p - 4) = 20 - 3 p$

Step 1.1.7

Apply the distributive property.

$24 - 16 p - 16 + 16 p - 3 p - 3 \cdot - 4 = 20 - 3 p$

Step 1.1.8

Multiply $- 3$ by $- 4$ .

$24 - 16 p - 16 + 16 p - 3 p + 12 = 20 - 3 p$

Step 1.2

Simplify by adding terms.

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Step 1.2.1

Combine the opposite terms in $24 - 16 p - 16 + 16 p - 3 p + 12$ .

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Step 1.2.1.1

Add $- 16 p$ and $16 p$ .

$24 + 0 - 16 - 3 p + 12 = 20 - 3 p$

Step 1.2.1.2

Add $24$ and $0$ .

$24 - 16 - 3 p + 12 = 20 - 3 p$

Step 1.2.2

Simplify by adding and subtracting.

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Step 1.2.2.1

Subtract $16$ from $24$ .

$8 - 3 p + 12 = 20 - 3 p$

Step 1.2.2.2

Add $8$ and $12$ .

$- 3 p + 20 = 20 - 3 p$

Step 2

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

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Step 2.1

Add $3 p$ to both sides of the equation.

$- 3 p + 20 + 3 p = 20$

Step 2.2

Combine the opposite terms in $- 3 p + 20 + 3 p$ .

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Step 2.2.1

Add $- 3 p$ and $3 p$ .

$0 + 20 = 20$

Step 2.2.2

Add $0$ and $20$ .

$20 = 20$

Step 3

Since $20 = 20$ , the equation will always be true for any value of $p$ .

All real numbers

Step 4

The result can be shown in multiple forms.

All real numbers

Interval Notation:

$(- \infty, \infty)$