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Solve for $x$ . $\newline$ $x + 3 \leq -6$ or $x - 19 \geq 1$ $\newline$ Write your answer as a compound inequality with integers. $\newline$ Choices: $\newline$ (A) $x \leq -9$ or $x \geq 20$ $\newline$ (B) $x \leq -3$ or $x \geq 20$ $\newline$ (C) $x \leq -3$ or $x \geq -18$ $\newline$ (D) $x \leq -9$ or $x \geq -18$

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Solve compound inequalities

Full solution

Q. Solve for

x

.

\newline

x + 3 \leq -6

or

x - 19 \geq 1

\newline

Write your answer as a compound inequality with integers.

\newline

Choices:

\newline

(A)

x \leq -9

or

x \geq 20

\newline

(B)

x \leq -3

or

x \geq 20

\newline

(C)

x \leq -3

or

x \geq -18

\newline

(D)

x \leq -9

or

x \geq -18

Solve First Part: Solve the first part of the compound inequality $x + 3 \leq -6$ . Which operation should we use to isolate $x$ ? In $x + 3$ , $3$ is being added to $x$ . Subtraction should be used to isolate $x$ . $x + 3 \leq -6$ $x + 3 - 3 \leq -6 - 3$ $x \leq -9$
Solve Second Part: Solve the second part of the compound inequality $x - 19 \geq 1$ . Which operation should we use to isolate $x$ ? In $x - 19$ , $19$ is being subtracted from $x$ . Addition should be used to isolate $x$ . $x - 19 \geq 1$ $x - 19 + 19 \geq 1 + 19$ $x \geq 20$
Combine Solutions: Combine the solutions from Step $1$ and Step $2$ to write the final compound inequality. $\newline$ The solution is $x \leq -9$ or $x \geq 20$ .

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