Finite Math Examples

$4 x - 8 (\frac{1}{2} x - 4) = 32$

Step 1

Simplify $4 x - 8 (\frac{1}{2} x - 4)$ .

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Step 1.1

Simplify each term.

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Step 1.1.1

Combine $\frac{1}{2}$ and $x$ .

$4 x - 8 (\frac{x}{2} - 4) = 32$

Step 1.1.2

Apply the distributive property.

$4 x - 8 \frac{x}{2} - 8 \cdot - 4 = 32$

Step 1.1.3

Cancel the common factor of $2$ .

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Step 1.1.3.1

Factor $2$ out of $- 8$ .

$4 x + 2 (- 4) \frac{x}{2} - 8 \cdot - 4 = 32$

Step 1.1.3.2

Cancel the common factor.

$4 x + 2 \cdot - 4 \frac{x}{2} - 8 \cdot - 4 = 32$

Step 1.1.3.3

Rewrite the expression.

$4 x - 4 x - 8 \cdot - 4 = 32$

Step 1.1.4

Multiply $- 8$ by $- 4$ .

$4 x - 4 x + 32 = 32$

Step 1.2

Simplify by adding terms.

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Step 1.2.1

Subtract $4 x$ from $4 x$ .

$0 + 32 = 32$

Step 1.2.2

Add $0$ and $32$ .

$32 = 32$

Step 2

Since $32 = 32$ , the equation will always be true for any value of $x$ .

All real numbers

Step 3

The result can be shown in multiple forms.

All real numbers

Interval Notation:

$(- \infty, \infty)$