Algebra Examples

$22 \geq x + 10 > 19$

Step 1

Solve $22 \geq x + 10$ for $x$ .

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Step 1.1

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

$x + 10 \leq 22$

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.

$x \leq 22 - 10$

Step 1.2.2

Subtract $10$ from $22$ .

$x \leq 12$

Step 2

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

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Step 2.1

Subtract $10$ from both sides of the inequality.

$x > 19 - 10$

Step 2.2

Subtract $10$ from $19$ .

$x > 9$

Step 3

Find the intersection of $x \leq 12$ and $x > 9$ .

$9 < x \leq 12$

Step 4

The result can be shown in multiple forms.

Inequality Form:

$9 < x \leq 12$

Interval Notation:

$(9, 12]$

Step 5