Question 25·Easy·Equivalent Expressions
Which expression is equivalent to ?
For expression-equivalence questions, first apply the distributive property to remove any parentheses by multiplying the outside number by each term inside. Then carefully combine like terms by adding or subtracting their coefficients, watching signs on negative numbers. Once simplified, match your final expression exactly—both the variable term and the constant term—to one of the choices, rather than trying to manipulate each choice separately.
Hints
Start by removing the parentheses
Focus first on simplifying . What operation connects the 5 with the expression in parentheses?
Distribute correctly to both terms
Multiply 5 by each term inside the parentheses: both and . What do you get for each part?
Combine like terms
After distributing, you will have two -terms and one constant term. Which terms have , and what happens when you add their coefficients?
Desmos Guide
Enter and simplify the original expression
In a Desmos expression line, type 5(3y - 2) + 4y. Desmos will automatically show a simplified algebraic form of this expression next to what you typed.
Match the simplified form to a choice
Compare the simplified expression that Desmos displays with the answer choices. Select the option whose expression is exactly the same as the simplified form shown by Desmos.
Step-by-step Explanation
Use the distributive property
Apply the distributive property to remove the parentheses in .
So the whole expression becomes:
Combine like terms
Now combine the -terms in .
- The like terms are and .
- Add their coefficients: , so the combined -term has coefficient .
- The constant term stays .
So you end up with a -term whose coefficient is and a constant term of .
Write the simplified expression and match the choice
Putting the combined -term and the constant together, the simplified expression is
Looking at the answer choices, this matches choice D, .