What you’ll learn
Generate equivalent expressions.
Key idea
Distribution can remove parentheses, and combining like terms can collect repeated variable parts or constants. Each step must preserve equality; do not combine unlike terms or discard a term.
For 3(x + 4) + 2x, distributing gives 3x + 12 + 2x, then combining the x-terms gives 5x + 12. Substitution is a quick check: at x = 1, both forms equal 17. One check cannot prove equivalence for all values, but it can catch many arithmetic mistakes.
Worked example
Enter the exact value or ordered values in the format requested below.
Generate a simplified linear expression equivalent to 2(x-3)+1x+2 for every x.
- Distribute 2(x-3) to 2x-6.
- Combine x terms and constants separately: (2+1)x+(-6+2)=3x-4, an all-input identity.
Answer: 3x-4
Quick Check
Evaluate a worked attempt at generate equivalent expressions, identify the first invalid step, and provide the correction.
A student rewrites 2(x-2)+2x-2: Step 1, distribute to 2x-2+2x-2. Step 2, combine to 4x-4. Locate the first invalid step and correct the expression.