Question

Determine whether the equation is always, sometimes, or never true?

1. 2(5x+4)=10x+6

2. 6x-12+2x=3+8x-15

Answers

1) 2(5x + 4) = 10x + 6

10x + 8 = 10x + 6

8 = 6 is false so the equation is never true

2) 6x - 12 + 2x = 3 + 8x - 15

8x - 12 = 8x - 12

-12 = -12 is true so the equation is always true, i.e., the solution is all numbers

#1

1. never

10x+8 is in equal to 10x+6

2. always

8x-12=8x-12

#2

1. 2(5x+4)=10x+6.........Multiply out the left side

10x + 8 = 10x + 6...........Never true, regardless of the value of x

2. 6x-12+2x=3+8x-15........Collect terms (simplify) on both sides

8x - 12 = 8x - 12...........Always true for any given value of x

No problem, right?

#3