Are Two Expressions Equal?
Aligned to 6.EE.A.4 — Common Core State Standards for Mathematics.
What this lesson teaches
Two expressions are equivalent if they give the same result for EVERY value of the variable. Testing one number can hint at this, but simplifying both is how you prove it.
Worked examples
Example 1
Are 3(x + 2) and 3x + 6 equivalent? Distribute the first: 3x + 6. They match, so yes — try x = 5: both give 21. ✓
Example 2
Are 2(x + 3) and 2x + 3 equivalent? Distributing gives 2x + 6, not 2x + 3, so no. Try x = 1: 8 versus 5.
Example 3
One counterexample settles it. Two expressions are equivalent only if they match for every value, not just a lucky one.
Practice questions
- Are 2x + 2x and 4x equivalent? Explain.
- Show whether 5(n − 1) equals 5n − 5.
- Test x = 3 to decide if 2(x + 3) and 2x + 3 are equivalent.
Watch the lesson
Every lesson comes with a video taught in English and Spanish — the same video the QR code in the printed workbook opens.
▶ Watch this lessonEn español
¿Son Iguales Dos Expresiones?
Dos expresiones son equivalentes si dan el mismo resultado para CADA valor de la variable. Probar un número puede sugerirlo, pero simplificar ambas es la forma de comprobarlo.
Ejemplo 1: ¿Son equivalentes 3(x + 2) y 3x + 6? Distribuye la primera: 3x + 6. Coinciden, así que sí; prueba con x = 5: ambas dan 21. ✓
Ejemplo 2: ¿Son equivalentes 2(x + 3) y 2x + 3? Distribuir da 2x + 6, no 2x + 3, así que no. Prueba con x = 1: 8 contra 5.
Ejemplo 3: Un solo contraejemplo lo resuelve. Dos expresiones son equivalentes solo si coinciden para todo valor, no solo para uno afortunado.
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