Question 199·Easy·Equivalent Expressions
Which expression is equivalent to ?
For questions asking which expression is equivalent to a given one, focus on combining like terms: group terms with the same variable, add or subtract only their numerical coefficients, and keep the variable part unchanged. Work systematically (all terms, then all terms, etc.), pay close attention to plus and minus signs, and then match your simplified result to the answer choices rather than trying to manipulate each choice separately.
Hints
Group similar terms
Separate the terms with from the terms with in . Which two terms involve ? Which two involve ?
Combine the terms first
Think of as . What number do you get for the coefficient of ?
Then combine the terms
Now think of as . What number multiplies after you combine them?
Rebuild the expression
After you have one term with and one term with , write them together and see which answer choice matches that expression.
Desmos Guide
Let Desmos simplify the expression
In an expression line, type 7p - 4p + 6q - 5q. Desmos will automatically show a simplified form of this expression next to what you typed.
Compare with the choices
Look at the simplified expression that Desmos displays and compare its terms and signs to each answer choice to see which one matches exactly.
Step-by-step Explanation
Identify like terms
Look at the expression .
- Terms with : and
- Terms with : and
Only like terms (same variable and power) can be combined.
Combine the terms
Focus on .
- Combine the coefficients:
- Keep the variable
So .
Combine the terms
Now focus on .
- Combine the coefficients:
- Keep the variable
So , which we usually just write as .
Write the simplified expression and match the choice
Replace the original groups of terms with the simplified ones:
- becomes
- becomes
So the whole expression is , which corresponds to choice D.