Finite Math Examples

$2 x - 4 < \frac{16 - x}{- 4}$

Step 1

Multiply both sides by $- 4$ .

$(2 x - 4) \cdot - 4 > \frac{16 - x}{- 4} \cdot - 4$

Step 2

Simplify.

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Step 2.1

Simplify the left side.

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Step 2.1.1

Simplify $(2 x - 4) \cdot - 4$ .

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Step 2.1.1.1

Apply the distributive property.

$2 x \cdot - 4 - 4 \cdot - 4 > \frac{16 - x}{- 4} \cdot - 4$

Step 2.1.1.2

Multiply.

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Step 2.1.1.2.1

Multiply $- 4$ by $2$ .

$- 8 x - 4 \cdot - 4 > \frac{16 - x}{- 4} \cdot - 4$

Step 2.1.1.2.2

Multiply $- 4$ by $- 4$ .

$- 8 x + 16 > \frac{16 - x}{- 4} \cdot - 4$

Step 2.2

Simplify the right side.

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Step 2.2.1

Simplify $\frac{16 - x}{- 4} \cdot - 4$ .

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Step 2.2.1.1

Cancel the common factor of $4$ .

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Step 2.2.1.1.1

Factor $4$ out of $- 4$ .

$- 8 x + 16 > \frac{16 - x}{4 (- 1)} \cdot - 4$

Step 2.2.1.1.2

Factor $4$ out of $- 4$ .

$- 8 x + 16 > \frac{16 - x}{4 \cdot - 1} \cdot (4 \cdot - 1)$

Step 2.2.1.1.3

Cancel the common factor.

$- 8 x + 16 > \frac{16 - x}{4 \cdot - 1} \cdot (4 \cdot - 1)$

Step 2.2.1.1.4

Rewrite the expression.

$- 8 x + 16 > \frac{16 - x}{- 1} \cdot - 1$

Step 2.2.1.2

Combine $\frac{16 - x}{- 1}$ and $- 1$ .

$- 8 x + 16 > \frac{(16 - x) \cdot - 1}{- 1}$

Step 2.2.1.3

Simplify the expression.

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Step 2.2.1.3.1

Move the negative one from the denominator of $\frac{(16 - x) \cdot - 1}{- 1}$ .

$- 8 x + 16 > - 1 \cdot ((16 - x) \cdot - 1)$

Step 2.2.1.3.2

Rewrite $- 1 \cdot ((16 - x) \cdot - 1)$ as $- ((16 - x) \cdot - 1)$ .

$- 8 x + 16 > - ((16 - x) \cdot - 1)$

Step 2.2.1.4

Apply the distributive property.

$- 8 x + 16 > - (16 \cdot - 1 - x \cdot - 1)$

Step 2.2.1.5

Multiply $16$ by $- 1$ .

$- 8 x + 16 > - (- 16 - x \cdot - 1)$

Step 2.2.1.6

Multiply $- x \cdot - 1$ .

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Step 2.2.1.6.1

Multiply $- 1$ by $- 1$ .

$- 8 x + 16 > - (- 16 + 1 x)$

Step 2.2.1.6.2

Multiply $x$ by $1$ .

$- 8 x + 16 > - (- 16 + x)$

Step 2.2.1.7

Apply the distributive property.

$- 8 x + 16 > - - 16 - x$

Step 2.2.1.8

Simplify the expression.

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Step 2.2.1.8.1

Multiply $- 1$ by $- 16$ .

$- 8 x + 16 > 16 - x$

Step 2.2.1.8.2

Reorder $16$ and $- x$ .

$- 8 x + 16 > - x + 16$

Step 3

Solve for $x$ .

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Step 3.1

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

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Step 3.1.1

Add $x$ to both sides of the inequality.

$- 8 x + 16 + x > 16$

Step 3.1.2

Add $- 8 x$ and $x$ .

$- 7 x + 16 > 16$

Step 3.2

Move all terms not containing $x$ to the right side of the inequality.

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Step 3.2.1

Subtract $16$ from both sides of the inequality.

$- 7 x > 16 - 16$

Step 3.2.2

Subtract $16$ from $16$ .

$- 7 x > 0$

Step 3.3

Divide each term in $- 7 x > 0$ by $- 7$ and simplify.

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Step 3.3.1

Divide each term in $- 7 x > 0$ by $- 7$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- 7 x}{- 7} < \frac{0}{- 7}$

Step 3.3.2

Simplify the left side.

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Step 3.3.2.1

Cancel the common factor of $- 7$ .

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Step 3.3.2.1.1

Cancel the common factor.

$\frac{- 7 x}{- 7} < \frac{0}{- 7}$

Step 3.3.2.1.2

Divide $x$ by $1$ .

$x < \frac{0}{- 7}$

Step 3.3.3

Simplify the right side.

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Step 3.3.3.1

Divide $0$ by $- 7$ .

$x < 0$

Step 4

Convert the inequality to interval notation.

$(- \infty, 0)$

Step 5