Solve the System of Inequalities 15>=x+7 or x+7<19

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

Simplify the first inequality.

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

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

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

Subtract $7$ from both sides of the inequality.

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

Subtract $7$ from $15$ .

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

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

Subtract $7$ from both sides of the inequality.

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

Subtract $7$ from $19$ .

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

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

$x < 12$

The result can be shown in multiple forms.

Inequality Form:

$x < 12$

Interval Notation:

$(- \infty, 12)$