Question 94·Easy·Equivalent Expressions
Which of the following is equivalent to ?
For expression-equivalence questions with parentheses, first apply the distributive property carefully, multiplying the outer number by every term inside the parentheses, including negative signs. Then combine like terms by grouping variable terms together and constant numbers together, paying close attention to signs when adding or subtracting. Finally, match your simplified result to the answer choices, which is usually much faster and safer than trying to work backwards from each option.
Hints
Start with the parentheses
Focus first on the part . What property lets you multiply a number by everything inside parentheses?
Multiply carefully
Multiply 5 by and also by . Write out both products before adding 7.
Combine like terms
After distributing, you will have an expression with and two constant numbers. Combine the constants into a single number.
Desmos Guide
Enter the original expression
In Desmos, type y1 = 5(3x - 2) + 7 to represent the original expression as a function.
Enter each answer choice as a separate function
On new lines, enter y2 = 15x + 5, y3 = 15x - 3, y4 = 15x + 3, and y5 = 15x - 9. Each line will graph as a different-colored line.
Compare the graphs
Look at the graphs of and each of , , , and . The correct choice is the one whose line lies exactly on top of the line for for all -values (they will appear as a single line).
Step-by-step Explanation
Apply the distributive property
Start with the expression . Use the distributive property: multiply 5 by each term inside the parentheses:
So the whole expression becomes .
Combine like terms
Now simplify by combining the constant terms and :
So the expression becomes .
Match with the answer choices
We have simplified to .
Looking at the choices, is given as option B, so that is the equivalent expression.