Back to Explain intersection as solution — Problem 5 · Task Set 52

Exercises: Graph Intersections as Solutions

For graphical problems, identify the x-coordinate of each intersection as the solution. Always verify by substituting back into both sides of the original equation. Use graphing technology (Desmos or graphing calculator) where indicated.

Grade 9·18 problems·~40 min·Common Core Math - HS Algebra·standard·hsa-rei-d-11

Work through problems with immediate feedback

Fluency Practice

A student uses Desmos to solve $|x - 1| = 2x - 3$ by graphing $y = |x - 1|$ and $y = 2x - 3$ . The graphs appear to intersect at $x = 2$ and the student finds no other intersection in the standard window.

What should the student do before accepting $x = 2$ as the only solution?

Accept $x = 2$ immediately — once one solution is found, the equation is solved.

Zoom out to check whether the graphs intersect anywhere else, then verify each candidate by substitution.

Also check whether $x = -2$ is a solution, since absolute value equations always have two solutions.

Switch to the algebraic method to confirm there are no other solutions.