How do you solve #abs(2x+1) > 5#?

1 Answer
Don't Memorise
May 2, 2015

#abs(2x+1) > 5#

The Absolute Value tells us how far the number is from Zero.

This tells us that :

Either #2x + 1 >5# or #2x + 1 < -5#

#2x > 5 - 1# or #2x < -5 - 1#

#2x > 4# or #2x < -6#

#color(green)(x>2# or #color(green)(x < - 3#

To verify your answer , choose appropriate values of #x# and see if the inequality is satisfied

  • Say #x = 4# (A random number greater than 2)

Left hand side = #abs(2*4+1) = abs(8+1) = abs(9) = 9# (#>5#)

  • Say #x = -6#(A random number less than -3)

Left hand side = #abs(2*-6+1) = abs(-12+1) = abs(-11) = 11# (#>5#)

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