Solve for b. 7 -4 (C)-12 < b < -4 (D)b < -12 or b ≥ -4

Analyze Compound Inequality: Analyze the given compound inequality 7 < b + 19 < 15. Which operation should we use to isolate b? In b + 19, 19 is being added to b. Subtraction should be used to isolate b.Subtract 19 to Isolate: Subtract 19 from all parts of the inequality to solve for b. 7 < b + 19 < 15 7 - 19 < b + 19 - 19 < 15 - 19 -12 < b < -4Check Solution: Check the solution to ensure it makes sense. If b is -12, then b + 19 would be 7, which is not strictly greater than 7, so b must be greater than -12. If b is -4, then b + 19 would be 15, which is not strictly less than 15, so b must be less than -4. The solution -12 < b < -4 satisfies the original inequality.

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Solve for $b$ . $\newline$ 7 < b + 19 < 15 $\newline$ Write your answer as a compound inequality with integers. $\newline$ Choices: $\newline$ (A) -12 < b \leq -4 $\newline$ (B) b < -12 or b > -4 $\newline$ (C) -12 < b < -4 $\newline$ (D) b < -12 or $b \geq -4$

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Math Problems

Algebra 1

Solve compound inequalities

Full solution

Q. Solve for

b

\newline

7 < b + 19 < 15

\newline

Write your answer as a compound inequality with integers.

\newline

Choices:

\newline

(A)

-12 < b \leq -4

\newline

(B)

b < -12

b > -4

\newline

(C)

-12 < b < -4

\newline

(D)

b < -12

b \geq -4

Analyze Compound Inequality: Analyze the given compound inequality 7 < b + 19 < 15. Which operation should we use to isolate $b$ ? In $b + 19$ , $19$ is being added to $b$ . Subtraction should be used to isolate $b$ .
Subtract $19$ to Isolate: Subtract $19$ from all parts of the inequality to solve for $b$ .7 < b + 19 < 157 - 19 < b + 19 - 19 < 15 - 19-12 < b < -4
Check Solution: Check the solution to ensure it makes sense. $\newline$ If $b$ is $-12$ , then $b + 19$ would be $7$ , which is not strictly greater than $7$ , so $b$ must be greater than $-12$ . $\newline$ If $b$ is $-4$ , then $b + 19$ would be $-12$ $0$ , which is not strictly less than $-12$ $0$ , so $b$ must be less than $-4$ . $\newline$ The solution $-12$ $4$ satisfies the original inequality.