Simplify the expression: –2(x–4)–(2x+1)

Question
Which expression is equivalent to –2(x–4)–(2x+1)?

a. –3x + 7
b. –3x – 7
c. –4x + 7
d. –4x – 7
Answer
STEP 1:    You are given an algebraic expression which contains parentheses. Removing these parentheses is the first step to be done in simplifying the expression.

Consider –2(x – 4). The factor –2 is distributed over the difference x – 4. To remove the brackets in this term, first multiply -2 by x. Then, you get –2x. Multiply -2 by -4 next. The result that you get is –2x + 8.

STEP 2:    Now, you can follow the same method to remove the parentheses in –(2x + 1) and note that '–' is equivalent to –1:
removing the brackets in -(2x+1)
Put the new expressions back into the original expression.
expression with brackets removed
STEP 3:    You can see that the expression has like terms in it. So, the next move from your side should be to place these terms together.
arranging the like terms together
Simplify by combining the variable terms and then combining the constants.
simplify the expression

Since there are no more like terms left out that can be combined, it is sure that the result in the simplest form.

STEP 4:    Finally, pick the choice that matches with the answer. You can see that the correct choice is c.

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