Question

What are the two equations to set up to solve the equation |2x−3|=11

−2x−3=11 and 2x−3=−11−2x−3=11 and 2x−3=−11

2x+3=11 and 2x−3=−112x+3=11 and 2x−3=−11

2x−3=11 and 2x−3=−112x−3=11 and 2x−3=−11

2x+3=11 and 2x+3=−112x+3=11 and 2x+3=−11

Answer 1

Absolute value is the distance from 0. You may recall that absolute value is always positive; this is because distance is not negative. So, in this case, 11 is the distance, but there are two possible, equal distances from 0. 11 is one and -11 is the other. Just because -11 is a negative number does not mean the distance from 0 is -11 because distance is never negative. Therefore, we need to create two equations:

2x-3=11 and 2x-3=-11

These equations are really starting 2 times a number x minus 3 = 11, and 2 times a number x minus 3 = -11. So x will have two solutions to make the equation correct.