Plugging In and Back-Solving Techniques

ACT Math · Axiom Academy

LESSON Plugging In and Back-Solving Two number-testing shortcuts that turn abstract algebra into simple arithmetic — pick a number, compute, and let the answer choices reveal themselves When a question has variables in the answer choices — not just in the question — you can sidestep the algebra entirely. Pick a simple concrete number for the variable, compute the actual numeric answer, then plug that same number into each answer choice and see which one matches. Whichever choice matches for your number is the answer, because it has to match for every number. Watch it work below: with x = 4 , the expression x+2x+3x builds to a running total on the left while all five answer choices compute their own value with that same x=4 on the right — only one choice will land on the same number. Problem: If x is an even integer, what is the value of x+2x+3x ? A) x B) 3x C) 6x D) x+2 E) 6x+2 Algebraic method: x+2x+3x=6x — answer C. Plugging-in method: let x=4 . Then x+2x+3x = 4+8+12=24 . Testing the choices at x=4 : A gives 4 , B gives 12 , C gives 24 ✓, D gives 6 , E gives 26 . Only C matches — answer C, confirmed without ever simplifying the algebra. 2. Back-Solving: Testing the Answer Choices

This is the written version of the interactive lesson above. See the full ACT Math course.