Question

NEED THIS ASAP!!!!!!!!!!!!!

Three students were given the expression shown and were asked to take a common factor out of two of the terms.

Use the drop-down menus to complete the statements about whether each student's answer is an equivalent expression. Then choose an expression that is equivalent.

7-8x+22

Calvin: 7−2(4x+11)
Calvin's expression is (correct/incorrect) because .............

Greg: 7+14x
Greg's expression is (correct/incorrect) because ............

Ruben: 7+2(4x+11)
Ruben's expression is (correct/incorrect) because .

Equivalent Expression

The correct simplification of this expression is ...............

Answer 1

• Calvin: incorrect, sign error
• Greg: incorrect, has no relationship to the given expression
• Ruben: incorrect, sign error
• Equivalent expresssion: 7 92(4x -11)

Step-by-step explanation:

The two terms on the right, -8x and +22, have even coefficients, so a factor of 2 can be factored out. If we do that, then these two terms become ...

... 2(-8x/2 +22/2) = 2(-4x +11)

We could, instead, factor out -2 so the x-coefficient inside parentheses is positive:

... -2(-8x/-2 +22/-2) = -2(4x -11)

Note that the signs of the two terms inside parentheses are different no matter which way we do it.

Equivalent expressions

Calvin could have written: 7 -2(4x -11)

Ruben could have written: 7 +2(-4x +11)

Greg could have written: 8(2 -x) -1. He would have rearranged the expression to 16 -8x -1 before doing so.