Solve for a. 14 ≥ a + 6 > -12 Write your answer as a compound inequality with integers. Choices: (A)8 ≥ a > -18 (B)8 ≥ a > -6 (C)20 ≥ a > -18 (D)20 ≥ a > -6

Identify Operation for Isolation: 14 ≥ a + 6 > -12 Which operation should we use to isolate a? In a + 6, 6 is being added to a. Subtraction should be used to isolate a.Solve for a: 14 ≥ a + 6 > -12 Solve for a. 14 - 6 ≥ a + 6 - 6 > -12 - 6 8 ≥ a > -18Check Solution: Check the solution. Replace a with a number that is between 8 and -18 to see if it satisfies the original inequality. Let's take a = 0 as an example. 14 ≥ 0 + 6 > -12 14 ≥ 6 > -12 This is true, so our solution seems correct.

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Math Problems

Algebra 1

Solve compound inequalities

Full solution

Q. Solve for

a

\newline

14 \geq a + 6 > -12

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Write your answer as a compound inequality with integers.

\newline

Choices:

\newline

(A)

8 \geq a > -18

\newline

(B)

8 \geq a > -6

\newline

(C)

20 \geq a > -18

\newline

(D)

20 \geq a > -6

Identify Operation for Isolation: 14 \geq a + 6 > -12 $\newline$ Which operation should we use to isolate $a$ ? $\newline$ In $a + 6$ , $6$ is being added to $a$ . $\newline$ Subtraction should be used to isolate $a$ .
Solve for $a$ : 14 \geq a + 6 > -12 Solve for $a$ . 14 - 6 \geq a + 6 - 6 > -12 - 6 8 \geq a > -18
Check Solution: Check the solution. $\newline$ Replace $a$ with a number that is between $8$ and $-18$ to see if it satisfies the original inequality. $\newline$ Let's take $a = 0$ as an example. $\newline$ 14 \geq 0 + 6 > -12 $\newline$ 14 \geq 6 > -12 $\newline$ This is true, so our solution seems correct.