Solve for y. -5 ≤ y - 13 < 7 Write your answer as a compound inequality with integers. Choices: (A)-18 ≤ y < 20 (B)8 ≤ y < -6 (C)8 ≤ y < 20 (D)-18 ≤ y < -6

Analyze Inequality: Analyze the compound inequality -5 ≤ y - 13 < 7. Which operation should we use to isolate y? In y - 13, 13 is being subtracted from y. Addition should be used to isolate y.Addition Operation: Add 13 to all parts of the inequality -5 ≤ y - 13 < 7. -5 + 13 ≤ y - 13 + 13 < 7 + 13 8 ≤ y < 20Check Solution: Check the solution to ensure it makes sense. If we substitute a value of y that is within the range of 8 ≤ y < 20, it should satisfy the original inequality -5 ≤ y - 13 < 7. Let's check with y = 10: -5 ≤ 10 - 13 < 7 -5 ≤ -3 < 7 which is true.

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Math Problems

Algebra 1

Solve compound inequalities

Full solution

Q. Solve for

y

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-5 \leq y - 13 < 7

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Write your answer as a compound inequality with integers.

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Choices:

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(A)

-18 \leq y < 20

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(B)

8 \leq y < -6

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(C)

8 \leq y < 20

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(D)

-18 \leq y < -6

Analyze Inequality: Analyze the compound inequality -5 \leq y - 13 < 7. Which operation should we use to isolate $y$ ? In $y - 13$ , $13$ is being subtracted from $y$ . Addition should be used to isolate $y$ .
Addition Operation: Add $13$ to all parts of the inequality -5 \leq y - 13 < 7. $\newline$ -5 + 13 \leq y - 13 + 13 < 7 + 13 $\newline$ 8 \leq y < 20
Check Solution: Check the solution to ensure it makes sense. $\newline$ If we substitute a value of $y$ that is within the range of 8 \leq y < 20, it should satisfy the original inequality -5 \leq y - 13 < 7. $\newline$ Let's check with $y = 10$ : $\newline$ -5 \leq 10 - 13 < 7 $\newline$ -5 \leq -3 < 7 which is true.