Which expression is equivalent to ?
For distributive-property questions like this on the SAT, quickly multiply the number outside the parentheses by each term inside, one at a time, writing the intermediate results with the correct signs. Keep the variable with its coefficient, and apply sign rules carefully (negative × positive = negative, negative × negative = positive). Then combine the terms into a simplified expression and match it to the answer choices.
Hints
Use the distributive property
Think about how to remove the parentheses in . What should you do with the and each term inside the parentheses?
Multiply -5 by each term
First, multiply by . Then, separately, multiply by . Keep the variable with its coefficient when you multiply.
Watch the signs
When you multiply and , what sign should the result have? Recall the rule for multiplying two negative numbers.
Desmos Guide
Enter the original expression
In Desmos, type y = -5(2x - 7) to graph the original expression.
Graph each answer choice
On separate lines, enter y = -10x - 35, y = -5x - 7, y = -10x + 35, and y = -7x - 10. You will see up to five lines on the graph.
Compare the graphs or tables
Click the colored icon next to each equation to view a table of values or look at the graph. The correct choice is the one whose graph lies exactly on top of the graph of y = -5(2x - 7) (or has identical -values for all tested -values).
Step-by-step Explanation
Identify the operation needed
You are given the expression . The number is outside the parentheses, so you should use the distributive property: multiply by each term inside the parentheses.
Distribute -5 to each term inside the parentheses
Multiply by the first term :
Then multiply by the second term :
Be careful with signs: a negative times a negative is a positive.
Write the simplified expression
Combine the two results to rewrite the expression without parentheses:
So the expression equivalent to is .