Equations with Variables on Both Sides

Pre-Algebra · Axiom Academy

LESSON Variables on Both Sides Collect every variable term on one side and every number on the other — by subtracting the smaller variable term from both sides. Look at 3x + 5 = 2x + 9 . The variable x shows up on the left (as 3x ) and on the right (as 2x ). With x in two places, there s no single side to isolate it on yet. Variable terms — on both sides The two variable terms are 3x and 2x . Subtract the smaller one, 2x , from both sides. On the right, 2x - 2x cancels to nothing. On the left, 3x - 2x combines into a single x — so every variable term has migrated to one side. Subtract 2x from both sides — the right x -term vanishes Collecting the variables left us with x + 5 = 9 — a plain one-step equation. Now move the constant: subtract 5 from both sides. The +5 on the left cancels, and 9 - 5 gives the answer. Put x = 4 back into the original equation: the left side is 3(4) + 5 = 17 and the right side is 2(4) + 9 = 17 . Both sides equal 17 , so x = 4 is correct. You turned an equation with x on both sides into a single isolated x — by subtracting the smaller variable term from both sides, then solving what was left. Scroll up to revisit any step.

This is the written version of the interactive lesson above. See the full Pre-Algebra course.