Algebra Examples

$15 \geq x + 7$ or $x + 7 < 19$

Step 1

Simplify the first inequality.

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Step 1.1

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

$x + 7 \leq 15$ or $x + 7 < 19$

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 $7$ from both sides of the inequality.

$x \leq 15 - 7$ or $x + 7 < 19$

Step 1.2.2

Subtract $7$ from $15$ .

$x \leq 8$ or $x + 7 < 19$

Step 2

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

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Step 2.1

Subtract $7$ from both sides of the inequality.

$x \leq 8$ or $x < 19 - 7$

Step 2.2

Subtract $7$ from $19$ .

$x \leq 8$ or $x < 12$

Step 3

The union consists of all of the elements that are contained in each interval.

$x < 12$

Step 4

The result can be shown in multiple forms.

Inequality Form:

$x < 12$

Interval Notation:

$(- \infty, 12)$

Step 5