Question

8 + |x -2| = 8|x + 1| +5 = 24|x - 3|= -163|x +10| = 0

Answer 1

Given

(a) 8 + |x -2| = 8

(b) |x + 1| +5 = 2

(c) 4|x - 3|= -16

(d) 3|x +10| = 0

Find

x

Solution

(a) |x -2| = 0 . . . . . subtract 8

... x -2 = 0 . . . . . . . only one solution, because -0 = 0

... x = 2

(b) |x +1| = -3 . . . . subtract 5. No solution. (an absolute value cannot be negative)

(c) No solution. (see (b))

(d) |x +10| = 0 . . . . divide by 3

... x +10 = 0 . . . . . . one solution. (see (a))

... x = -10