Given the expression
which of the following expressions is equivalent?
For equivalent-expression problems that involve parentheses, first distribute any numbers (or coefficients) across the parentheses, paying close attention to negative signs, especially a minus in front of an entire parentheses group. After all parentheses are removed, combine like terms (all terms together and all constants together). If you are unsure, you can quickly test your result by plugging in a simple value for (like ) into both the original and your simplified expression to see if they match.
Hints
Start with distribution
Focus first on . How do you distribute the 4 to both terms inside the parentheses?
Be careful with the minus sign
Rewrite in a way that removes the parentheses. How does the minus sign affect both and ?
Combine like terms
After you remove all parentheses, group the terms together and the constant numbers together, then combine them.
Desmos Guide
Graph the original expression
In Desmos, type y = 4(2x - 3) - (x + 5) on one line. This creates the graph of the original expression.
Graph each answer choice for comparison
On separate lines, type y = 9x - 7, y = 7x - 17, y = 7x + 17, and y = 8x - 20. You will now see several lines on the same coordinate plane.
See which line matches the original
Look for the answer-choice line that lies exactly on top of the graph of y = 4(2x - 3) - (x + 5) for all values of . The matching line represents the equivalent expression.
Step-by-step Explanation
Distribute the 4 in the first parentheses
Start with the expression:
Distribute the 4 to both and :
So becomes , and the whole expression is now:
Handle the minus sign before the second parentheses
The expression means you are subtracting both and .
This is the same as multiplying by :
So the full expression becomes:
Combine like terms to get the simplified expression
Now combine the terms and the constant terms separately:
So the simplified, equivalent expression is:
This matches answer choice B.