Algebra Examples

$\frac{3 x - 2}{- 5} > x - 5$

Step 1

Multiply both sides by $- 5$ .

$\frac{3 x - 2}{- 5} \cdot - 5 < (x - 5) \cdot - 5$

Step 2

Simplify.

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Step 2.1

Simplify the left side.

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Step 2.1.1

Simplify $\frac{3 x - 2}{- 5} \cdot - 5$ .

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Step 2.1.1.1

Cancel the common factor of $5$ .

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Step 2.1.1.1.1

Factor $5$ out of $- 5$ .

$\frac{3 x - 2}{5 (- 1)} \cdot - 5 < (x - 5) \cdot - 5$

Step 2.1.1.1.2

Factor $5$ out of $- 5$ .

$\frac{3 x - 2}{5 \cdot - 1} \cdot (5 \cdot - 1) < (x - 5) \cdot - 5$

Step 2.1.1.1.3

Cancel the common factor.

$\frac{3 x - 2}{5 \cdot - 1} \cdot (5 \cdot - 1) < (x - 5) \cdot - 5$

Step 2.1.1.1.4

Rewrite the expression.

$\frac{3 x - 2}{- 1} \cdot - 1 < (x - 5) \cdot - 5$

Step 2.1.1.2

Combine $\frac{3 x - 2}{- 1}$ and $- 1$ .

$\frac{(3 x - 2) \cdot - 1}{- 1} < (x - 5) \cdot - 5$

Step 2.1.1.3

Simplify the expression.

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Step 2.1.1.3.1

Move the negative one from the denominator of $\frac{(3 x - 2) \cdot - 1}{- 1}$ .

$- 1 \cdot ((3 x - 2) \cdot - 1) < (x - 5) \cdot - 5$

Step 2.1.1.3.2

Rewrite $- 1 \cdot ((3 x - 2) \cdot - 1)$ as $- ((3 x - 2) \cdot - 1)$ .

$- ((3 x - 2) \cdot - 1) < (x - 5) \cdot - 5$

Step 2.1.1.4

Apply the distributive property.

$- (3 x \cdot - 1 - 2 \cdot - 1) < (x - 5) \cdot - 5$

Step 2.1.1.5

Multiply.

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Step 2.1.1.5.1

Multiply $- 1$ by $3$ .

$- (- 3 x - 2 \cdot - 1) < (x - 5) \cdot - 5$

Step 2.1.1.5.2

Multiply $- 2$ by $- 1$ .

$- (- 3 x + 2) < (x - 5) \cdot - 5$

Step 2.1.1.6

Apply the distributive property.

$- (- 3 x) - 1 \cdot 2 < (x - 5) \cdot - 5$

Step 2.1.1.7

Multiply.

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Step 2.1.1.7.1

Multiply $- 3$ by $- 1$ .

$3 x - 1 \cdot 2 < (x - 5) \cdot - 5$

Step 2.1.1.7.2

Multiply $- 1$ by $2$ .

$3 x - 2 < (x - 5) \cdot - 5$

Step 2.2

Simplify the right side.

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Step 2.2.1

Simplify $(x - 5) \cdot - 5$ .

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Step 2.2.1.1

Apply the distributive property.

$3 x - 2 < x \cdot - 5 - 5 \cdot - 5$

Step 2.2.1.2

Simplify the expression.

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Step 2.2.1.2.1

Move $- 5$ to the left of $x$ .

$3 x - 2 < - 5 \cdot x - 5 \cdot - 5$

Step 2.2.1.2.2

Multiply $- 5$ by $- 5$ .

$3 x - 2 < - 5 x + 25$

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 $5 x$ to both sides of the inequality.

$3 x - 2 + 5 x < 25$

Step 3.1.2

Add $3 x$ and $5 x$ .

$8 x - 2 < 25$

Step 3.2

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

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Step 3.2.1

Add $2$ to both sides of the inequality.

$8 x < 25 + 2$

Step 3.2.2

Add $25$ and $2$ .

$8 x < 27$

Step 3.3

Divide each term in $8 x < 27$ by $8$ and simplify.

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Step 3.3.1

Divide each term in $8 x < 27$ by $8$ .

$\frac{8 x}{8} < \frac{27}{8}$

Step 3.3.2

Simplify the left side.

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Step 3.3.2.1

Cancel the common factor of $8$ .

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Step 3.3.2.1.1

Cancel the common factor.

$\frac{8 x}{8} < \frac{27}{8}$

Step 3.3.2.1.2

Divide $x$ by $1$ .

$x < \frac{27}{8}$

Step 4

The result can be shown in multiple forms.

Inequality Form:

$x < \frac{27}{8}$

Interval Notation:

$(- \infty, \frac{27}{8})$