AlgebraVery hardGreatest integer after distributing a negative
Algebra practice question
What is the greatest integer value of x that satisfies −3(x − 2) > 2x − 4?
Answer: 1
−3x + 6 > 2x − 4 gives 10 > 5x, so x < 2. The greatest integer is 1.
Common wrong answers
- If you answered 0
- 0 comes from distributing −3 only over x.
- If you answered 2
- 2 makes both sides 0, and 0 > 0 is false.
- If you answered -1
- −1 satisfies it but is not the greatest.
More Algebra questions
- Very hard
For what value of c does the system 3x − 2y = 8 and 9x + cy = 5 have no solution? - Very hard
In the system 5x + 4y = 32 and 3x − 2y = 6, what is the value of 8x + 2y? - Very hard
The solution set of the inequality |ax − b| ≤ 6, where a and b are constants and a > 0, is 3 ≤ x ≤ 9. What is … - Very hard
The function f is linear, and for every value of x, f(x + 2) − f(x) = 6. If f(5) = 4, what is the value of f(0… - Very hard
In the system of equations 2x + 3y = 12 and 5x − 2y = k, where k is a constant, the solution (x, y) satisfies … - Very hard
In the xy-plane, the system of equations kx + 6y = 12 and 2x + (k − 1)y = 6, where k is a constant, has infini…
Not affiliated with the College Board. SAT is a trademark of the College Board.