Pre-Algebra Examples

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

Step 1

Simplify $5 (x - 5)$ .

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Step 1.1

Rewrite.

$0 + 0 + 5 (x - 5) < 3 (2 x - 1)$

Step 1.2

Simplify by adding zeros.

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

Step 1.3

Apply the distributive property.

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

Step 1.4

Multiply $5$ by $- 5$ .

$5 x - 25 < 3 (2 x - 1)$

Step 2

Simplify $3 (2 x - 1)$ .

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Step 2.1

Apply the distributive property.

$5 x - 25 < 3 (2 x) + 3 \cdot - 1$

Step 2.2

Multiply.

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Step 2.2.1

Multiply $2$ by $3$ .

$5 x - 25 < 6 x + 3 \cdot - 1$

Step 2.2.2

Multiply $3$ by $- 1$ .

$5 x - 25 < 6 x - 3$

Step 3

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

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Step 3.1

Subtract $6 x$ from both sides of the inequality.

$5 x - 25 - 6 x < - 3$

Step 3.2

Subtract $6 x$ from $5 x$ .

$- x - 25 < - 3$

Step 4

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

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Step 4.1

Add $25$ to both sides of the inequality.

$- x < - 3 + 25$

Step 4.2

Add $- 3$ and $25$ .

$- x < 22$

Step 5

Divide each term in $- x < 22$ by $- 1$ and simplify.

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Step 5.1

Divide each term in $- x < 22$ by $- 1$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- x}{- 1} > \frac{22}{- 1}$

Step 5.2

Simplify the left side.

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Step 5.2.1

Dividing two negative values results in a positive value.

$\frac{x}{1} > \frac{22}{- 1}$

Step 5.2.2

Divide $x$ by $1$ .

$x > \frac{22}{- 1}$

Step 5.3

Simplify the right side.

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Step 5.3.1

Divide $22$ by $- 1$ .

$x > - 22$

Step 6

The result can be shown in multiple forms.

Inequality Form:

$x > - 22$

Interval Notation:

$(- 22, \infty)$