AlgebraEasy–MediumDividing an inequality by a negative
Algebra practice question
If −3x ≤ 12, which of the following describes every possible value of x?
- A. x ≥ −4Correct
- B. x ≤ −4
- C. x ≥ 4
- D. x ≤ 4
Answer: A. x ≥ −4
Divide both sides by −3. Dividing by a negative number reverses the inequality: x ≥ −4. Check with x = 0: −3(0) = 0 ≤ 12, true, and 0 ≥ −4 — consistent.
Why the other answers are wrong
- B. x ≤ −4
- You divided by −3 but didn't reverse the sign. Test x = 0: it satisfies the original (0 ≤ 12) but not x ≤ −4, so this can't be right.
- C. x ≥ 4
- The sign of the answer is wrong: 12 divided by −3 is −4, not 4.
- D. x ≤ 4
- Both the number's sign and the inequality direction are off. 12 / (−3) = −4, and the division by a negative reverses ≤ to ≥.
More Algebra questions
- Easy–Medium
A line passes through the points (0, 3) and (2, 7). What is the slope of the line? - Easy–Medium
A gym charges a $25 one-time signup fee plus $15 per month. Which equation gives the total cost C, in dollars,… - Easy–Medium
If 5(x − 2) = 3x + 4, what is the value of x? - Easy–Medium
A taxi charges a $3.50 base fare plus $2.25 per mile. If a ride costs $19.25 total, how many miles was the rid… - Easy–Medium
The equation of a line is 3x + 2y = 12. What is the y-coordinate of the point where the line crosses the y-axi… - Easy–Medium
A line in the xy-plane passes through the points (1, 5) and (4, 11). What is the y-intercept of the line?
Not affiliated with the College Board. SAT is a trademark of the College Board.