Solve for h. h + 5 ≤ 7 or h - 1 > 7 Write your answer as a compound inequality with integers. Choices: (A)h ≤ 12 or h > 6 (B)h ≤ 12 or h > 8 (C)h ≤ 2 or h > 8 (D)h ≤ 2 or h > 6

Isolate h ≤ 2: Solve the first part of the compound inequality. We have h + 5 ≤ 7. To isolate h, we need to subtract 5 from both sides of the inequality. h + 5 - 5 ≤ 7 - 5 h ≤ 2Isolate h > 8: Solve the second part of the compound inequality. We have h - 1 > 7. To isolate h, we need to add 1 to both sides of the inequality. h - 1 + 1 > 7 + 1 h > 8Combine solutions: Combine the solutions from Step 1 and Step 2 to write the final compound inequality. The solution is h ≤ 2 or h > 8.

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Math Problems

Algebra 1

Solve compound inequalities

Full solution

Q. Solve for

h

\newline

h + 5 \leq 7

h - 1 > 7

\newline

Write your answer as a compound inequality with integers.

\newline

Choices:

\newline

(A)

h \leq 12

h > 6

\newline

(B)

h \leq 12

h > 8

\newline

(C)

h \leq 2

h > 8

\newline

(D)

h \leq 2

h > 6

Isolate $h \leq 2$ : Solve the first part of the compound inequality. $\newline$ We have $h + 5 \leq 7$ . To isolate $h$ , we need to subtract $5$ from both sides of the inequality. $\newline$ $h + 5 - 5 \leq 7 - 5$ $\newline$ $h \leq 2$
Isolate h > 8: Solve the second part of the compound inequality. $\newline$ We have h - 1 > 7. To isolate $h$ , we need to add $1$ to both sides of the inequality. $\newline$ h - 1 + 1 > 7 + 1 $\newline$ h > 8
Combine solutions: Combine the solutions from Step $1$ and Step $2$ to write the final compound inequality. $\newline$ The solution is $h \leq 2$ or h > 8.