AlgebraHardInequality with x on both sides and a negative coefficient
Algebra practice question
Which of the following describes all solutions of 7 − 3x ≤ 2x − 8?
- A. x ≥ 3Correct
- B. x ≤ 3
- C. x ≥ −3
- D. x ≤ 15
Answer: A. x ≥ 3
Add 3x and 8: 15 ≤ 5x, so x ≥ 3.
Why the other answers are wrong
- B. x ≤ 3
- x ≤ 3 reverses the direction; check x = 2: 1 ≤ −4 is false.
- C. x ≥ −3
- x ≥ −3 mishandles the constants (7 + 8 = 15, not −15).
- D. x ≤ 15
- x ≤ 15 forgets to divide by 5 and reverses the direction.
More Algebra questions
- Hard
For how many integer values of x is −2 < (x − 5)/3 ≤ 1 true? - Hard
The system 2x + 3y = 6 and 4x + 6y = k has infinitely many solutions. What is the value of k? - Hard
Which of the following is the complete solution set to |x − 4| < 6? - Hard
A student has $40 to spend on notebooks costing $4 each and pens costing $2 each, and wants at least 12 items … - Hard
What is the least whole number of minutes of international calling in a month for which the total monthly cost… - Hard
How many liters of the 30% acid solution did the technician use?
Not affiliated with the College Board. SAT is a trademark of the College Board.