SOLUTION: Solve the equation |x+1| + |2x-3| = 8.

Question 1184798: Solve the equation |x+1| + |2x-3| = 8.
Found 2 solutions by MathLover1, greenestamps:
Answer by MathLover1(20850) (Show Source): You can put this solution on YOUR website!

or

or

Answer by greenestamps(13203) (Show Source): You can put this solution on YOUR website!

For x<-1, ; for x>-1, .

For x<3/2, ; for x>3/2< .

To solve the equation then, we need to consider three intervals of possible values for x: (1) x less than -1; (2) x between -1 and 3/2; and (3) x greater than 3/2.

Solve the equation on each of those intervals, remembering that any "solution" we get has to be in the interval we are working in.

(1) x less than -1

Since our solution x=-2 is in the interval x<-1, it is a solution; we can easily check that:

(2) x between -1 and 3/2

That solution is NOT in the interval we are working in; it is not a solution.

(3) x greater than 3/2

That solution is in the interval we are working in, so it is a solution.

ANSWERS: x=-2; x=10/3

A graph, showing abs(x+1)+abs(2x-3) (red) = 8 (green) at x=-2 and at x=10/3....

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