Algebra Examples

$4 \geq x + 10$ and $18 \geq x + 10$

Step 1

Simplify the first inequality.

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Step 1.1

Rewrite so $x$ is on the left side of the inequality.

$x + 10 \leq 4$

Step 1.2

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

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Step 1.2.1

Subtract $10$ from both sides of the inequality.

$x \leq 4 - 10$

Step 1.2.2

Subtract $10$ from $4$ .

$x \leq - 6$

Step 2

Simplify the second inequality.

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Step 2.1

Rewrite so $x$ is on the left side of the inequality.

$x + 10 \leq 18$

Step 2.2

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

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Step 2.2.1

Subtract $10$ from both sides of the inequality.

$x \leq 18 - 10$

Step 2.2.2

Subtract $10$ from $18$ .

$x \leq 8$

Step 3

The intersection consists of the elements that are contained in both intervals.

$x \leq - 6$

Step 4

The result can be shown in multiple forms.

Inequality Form:

$x \leq - 6$

Interval Notation:

$(- \infty, - 6]$

Step 5