Solving a Linear Inequality
Question
Answer choices
- x ≤ 4
- x < 4
- x > 4
- x ≥ 4
- x = 4
B Correct answer: B) x < 4
Set up the problem carefully before computing. Solve like a linear equation, but if you multiply or divide by a negative number, flip the inequality sign.
Carry the arithmetic through one step at a time, double-checking signs and units. The ACT writes wrong answers to catch the most common slips, so an answer that "looks right" without verification is risky.
Plug the answer back into the original expression as a sanity check whenever the problem allows. If the substitution does not balance, you have made an arithmetic mistake earlier in the work.
The underlying rule
Subtract 1: 4x > 15. Divide by 4: x > 3.75. Among the choices, the equivalent condition is x > 4 because 3.75 < 4.
Why each wrong answer is wrong
- A) x ≤ 4: A common arithmetic or sign error leads to this value; carefully redo the calculation.
- C) x > 4: A common arithmetic or sign error leads to this value; carefully redo the calculation.
- D) x ≥ 4: A common arithmetic or sign error leads to this value; carefully redo the calculation.
- E) x = 4: A common arithmetic or sign error leads to this value; carefully redo the calculation.
Study tip
Inequalities solve like equations — except multiplying or dividing both sides by a negative number flips the inequality direction.
More Hard Elementary Algebra
- Solving a Linear EquationIf 4x + 7 = 31, what is the value of x?
- Multiplying Binomials (FOIL)Expand and simplify: (2x + 1)(1x + 2).
- Evaluating an Algebraic ExpressionIf x = 4, what is the value of 3x^2 + 3x?
- Solving a Linear InequalitySolve for x: 3x + 1 > 6.
- Solving a Linear EquationIf 5x + 7 = 22, what is the value of x?