Strategic Solving

Algebra 1 · Axiom Academy

A reliable, repeatable order for solving multi-step equations — and how to dodge the mistakes that derail most attempts. Before moving anything across the equals sign, clean up each side on its own. That means carrying out any distribution and then combining like terms . Watch the animation distribute the 3 across the parentheses, then merge the two loose constants into one. Distribute the 3 across (x + 2) Combine the constants: +6 and −5 make +1 Now that each side is tidy, get the term that holds the variable — here 3x — alone on its side. Use an inverse operation to send the leftover constant to the other side. Since the 3x is being followed by +1 , you subtract 1 from both sides . The variable term stands alone, but x still wears a coefficient of 3 . Because that 3 is multiplying the x , the inverse is to divide both sides by 3 . The coefficient cancels and the variable is finally by itself. ! Common Pitfall: The Negative Sign The plan only works if Step 1 is done correctly — and the most common Step 1 error is mishandling a negative in front of parentheses. When a negative number is distributed, it must multiply every term inside. Watch the wrong shortcut and the correct distribution side by side on 5 - 2(x + 3) = 7 . Combining the 5 and the 2 first, as if they were like terms. The -2 is glued to the parentheses by multiplication — distribute it across both terms.

This is the written version of the interactive lesson above. See the full Algebra 1 course.