Algebra Examples

$5 (x - 2) \leq 4 x - 5$

Step 1

Simplify $5 (x - 2)$ .

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Step 1.1

Rewrite.

$0 + 0 + 5 (x - 2) \leq 4 x - 5$

Step 1.2

Simplify by adding zeros.

$5 (x - 2) \leq 4 x - 5$

Step 1.3

Apply the distributive property.

$5 x + 5 \cdot - 2 \leq 4 x - 5$

Step 1.4

Multiply $5$ by $- 2$ .

$5 x - 10 \leq 4 x - 5$

Step 2

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

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Step 2.1

Subtract $4 x$ from both sides of the inequality.

$5 x - 10 - 4 x \leq - 5$

Step 2.2

Subtract $4 x$ from $5 x$ .

$x - 10 \leq - 5$

Step 3

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

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Step 3.1

Add $10$ to both sides of the inequality.

$x \leq - 5 + 10$

Step 3.2

Add $- 5$ and $10$ .

$x \leq 5$

Step 4

The result can be shown in multiple forms.

Inequality Form:

$x \leq 5$

Interval Notation:

$(- \infty, 5]$