Lessons · Quantitative Reasoning

CLT Quantitative Reasoning · Lesson

Linear equations

Solve for the unknown by doing the same thing to both sides until it stands alone. Some questions ask for an expression, such as 2x + 1, rather than x itself.

How to do it
  1. Clear parentheses and fractions first (multiply every term by the denominator).
  2. Collect the variable on one side and the numbers on the other.
  3. Divide by the coefficient. Then reread what the question asks for.
  4. Stuck, or short of time? Plug in the choices. The CLT has no calculator, so start with a middle choice: put it into the equation and see if both sides match.
Example

Q. If 3(x − 4) + 5 = 2x + 9, what is x?

Answer 16

3x − 12 + 5 = 2x + 9, so 3x − 7 = 2x + 9, so x = 16. Check: 3(12) + 5 = 41 and 2(16) + 9 = 41.

Traps
  • Answering x when the question asked for 2x or x + 3. Circle what is asked before you start.
  • Distributing a minus sign to only the first term: −(x − 4) is −x + 4.
Practice it

Every practice question comes with a full explanation, including why each wrong choice is wrong. Free, with no account.