Question

solve the following linear equation. Identify the equation is an identity contradiction or conditional equation. 2(y+1)-4(y-3)=6y+14-8y

Answer 1

Our equation is 2(y+1)-4(y-3)=6y+14-8y and our goal is to get y on one side and not y on the other.

2 (y+1) - 4 (y - 3) = 6y + 14 - 8y

2y + 2 - 4y + 12 = 6y + 14 - 8y     <-- apply distribution on the left side to both pairs

-2y + 14 = 6y + 14 - 8y      <--- simplify the left side and collect like terms

-2y + 14 = -2y + 14           <--- simplify the right side

-2y = -2y                          <--- subtract 14 on both sides

y = y                              <----- divide both sides by -2

We have that y is equal to y, a statement that's always true.

Thus the equation is an identity and is true for all values of y.