Algebra Examples

$\frac{X}{4} + 4 < 3$ or $- x + 2 < 2$

Step 1

Simplify the first inequality.

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Step 1.1

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

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Step 1.1.1

Subtract $4$ from both sides of the inequality.

$\frac{X}{4} < 3 - 4$ or $- x + 2 < 2$

Step 1.1.2

Subtract $4$ from $3$ .

$\frac{X}{4} < - 1$ or $- x + 2 < 2$

Step 1.2

Multiply both sides by $4$ .

$\frac{X}{4} \cdot 4 < - 1 \cdot 4$ or $- x + 2 < 2$

Step 1.3

Simplify.

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Step 1.3.1

Simplify the left side.

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Step 1.3.1.1

Cancel the common factor of $4$ .

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Step 1.3.1.1.1

Cancel the common factor.

$\frac{X}{4} \cdot 4 < - 1 \cdot 4$ or $- x + 2 < 2$

Step 1.3.1.1.2

Rewrite the expression.

$X < - 1 \cdot 4$ or $- x + 2 < 2$

Step 1.3.2

Simplify the right side.

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Step 1.3.2.1

Multiply $- 1$ by $4$ .

$X < - 4$ or $- x + 2 < 2$

Step 2

Simplify the second inequality.

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Step 2.1

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

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Step 2.1.1

Subtract $2$ from both sides of the inequality.

$X < - 4$ or $- x < 2 - 2$

Step 2.1.2

Subtract $2$ from $2$ .

$X < - 4$ or $- x < 0$

Step 2.2

Divide each term in $- x < 0$ by $- 1$ and simplify.

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Step 2.2.1

Divide each term in $- x < 0$ by $- 1$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$X < - 4$ or $\frac{- x}{- 1} > \frac{0}{- 1}$

Step 2.2.2

Simplify the left side.

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Step 2.2.2.1

Dividing two negative values results in a positive value.

$X < - 4$ or $\frac{x}{1} > \frac{0}{- 1}$

Step 2.2.2.2

Divide $x$ by $1$ .

$X < - 4$ or $x > \frac{0}{- 1}$

Step 2.2.3

Simplify the right side.

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Step 2.2.3.1

Divide $0$ by $- 1$ .

$X < - 4$ or $x > 0$

Step 3