Solve for q. q + 15 < 19 or q - 6 ≥ 4 Write your answer as a compound inequality with integers. Choices: (A)4 ≤ q ≤ 10 (B)4 < q ≤ 10 (C)q ≤ 4 or q ≥ 10 (D)q < 4 or q ≥ 10

Solve first inequality: First, let's solve the inequality q + 15 < 19. To isolate q, we need to subtract 15 from both sides of the inequality. q + 15 - 15 < 19 - 15 q < 4Solve second inequality: Now, let's solve the inequality q - 6 ≥ 4. To isolate q, we need to add 6 to both sides of the inequality. q - 6 + 6 ≥ 4 + 6 q ≥ 10Final result: We have two separate inequalities from the original compound inequality: q < 4 or q ≥ 10 This means q can be any value less than 4 or any value greater than or equal to 10.

Home

Math Problems

Algebra 1

Solve compound inequalities

Full solution

Q. Solve for

q

\newline

q + 15 < 19

q - 6 \geq 4

\newline

Write your answer as a compound inequality with integers.

\newline

Choices:

\newline

(A)

4 \leq q \leq 10

\newline

(B)

4 < q \leq 10

\newline

(C)

q \leq 4

q \geq 10

\newline

(D)

q < 4

q \geq 10

Solve first inequality: First, let's solve the inequality q + 15 < 19. To isolate $q$ , we need to subtract $15$ from both sides of the inequality. q + 15 - 15 < 19 - 15 q < 4
Solve second inequality: Now, let's solve the inequality $q - 6 \geq 4$ . $\newline$ To isolate $q$ , we need to add $6$ to both sides of the inequality. $\newline$ $q - 6 + 6 \geq 4 + 6$ $\newline$ $q \geq 10$
Final result: We have two separate inequalities from the original compound inequality: $\newline$ q < 4 or $q \geq 10$ $\newline$ This means $q$ can be any value less than $4$ or any value greater than or equal to $10$ .