Solve for b. b + 3 -4 Write your answer as a compound inequality with integers. Choices: (A)b ≤ 0 or b > 3 (B)b ≤ 0 or b ≥ 3 (C)b 3

Isolate b in first inequality: We have two inequalities to solve: b + 3 -4. Let's start with the first inequality. To isolate b, we need to subtract 3 from both sides of the inequality b + 3 -4. To isolate b, we need to add 7 to both sides of the inequality b - 7 > -4. b - 7 + 7 > -4 + 7 b > 3Solution to compound inequality: We have now solved both inequalities. The solution to the compound inequality is: b 3 This matches one of the given choices.

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Math Problems

Algebra 1

Solve compound inequalities

Full solution

Q. Solve for

b

\newline

b + 3 < 3

b - 7 > -4

\newline

Write your answer as a compound inequality with integers.

\newline

Choices:

\newline

(A)

b \leq 0

b > 3

\newline

(B)

b \leq 0

b \geq 3

\newline

(C)

b < 0

b \geq 3

\newline

(D)

b < 0

b > 3

Isolate $b$ in first inequality: We have two inequalities to solve: b + 3 < 3 and b - 7 > -4. Let's start with the first inequality. $\newline$ To isolate $b$ , we need to subtract $3$ from both sides of the inequality b + 3 < 3. $\newline$ b + 3 - 3 < 3 - 3 $\newline$ b < 0
Isolate $b$ in second inequality: Now let's solve the second inequality: b - 7 > -4. To isolate $b$ , we need to add $7$ to both sides of the inequality b - 7 > -4. b - 7 + 7 > -4 + 7 b > 3
Solution to compound inequality: We have now solved both inequalities. The solution to the compound inequality is: $\newline$ b < 0 or b > 3 $\newline$ This matches one of the given choices.