DDesmos SAT Prep
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Backsolving Answer Choices

Test answer choices numerically instead of solving algebraically.

The Desmos trick

When an equation looks messy, don't solve it by hand — graph both sides as separate functions, or just substitute each answer choice into the equation using the table feature and see which one makes both sides equal.

  • Graph the left and right sides as two separate expressions and find where they intersect
  • Or: build a table, list the answer choices as x-values, and check which output satisfies the equation
  • Watch out for extraneous solutions with square roots — always verify in the original equation

Practice questions

Q1If 2(x - 3) + 5 = 3x - 4, which value of x satisfies the equation?
Medium
Q2Which value of x is a solution to the equation sqrt(x + 9) = x - 3?
Hard
Q3If 4(x + 2) - 3 = 2x + 9, which value of x satisfies the equation?
Medium
Q4Which value of x is a solution to the equation sqrt(3x + 1) = x - 1?
Hard