Which expression is equivalent to $8-(6 r+2)$?
A. $-6 r+6$
B. $2 r+2$
C. $6 r+15$
D. $-6 r+10$
Answer (1)
Distribute the negative sign: 8 − ( 6 r + 2 ) = 8 − 6 r − 2 .
Combine like terms: 8 − 6 r − 2 = 6 − 6 r .
Rewrite the expression: 6 − 6 r = − 6 r + 6 .
The equivalent expression is − 6 r + 6 .
Explanation
Understanding the problem We are given the expression 8 − ( 6 r + 2 ) and asked to find an equivalent expression from the given choices.
Plan of action To find the equivalent expression, we need to distribute the negative sign and combine like terms.
Distributing the negative sign First, distribute the negative sign: 8 − ( 6 r + 2 ) = 8 − 6 r − 2
Combining like terms Next, combine the constant terms: 8 − 6 r − 2 = 8 − 2 − 6 r = 6 − 6 r
Simplified expression So the simplified expression is 6 − 6 r , which can also be written as − 6 r + 6 .
Finding the equivalent expression Comparing this with the given choices, we see that − 6 r + 6 is one of the options.
Examples
Understanding how to simplify algebraic expressions like this is useful in many real-world situations. For example, if you are calculating the total cost of items with a discount, you might need to simplify an expression to find the final price. Suppose you have a coupon that gives you a discount on each item you buy. The expression might represent the original price minus the discount, and simplifying it helps you quickly calculate the total cost.
