1. / 2/3x-4 /+20<10
2. 3 /2x+4/ -24=12
rewrite as single inequality involving absolute value
1. x<negative2 or x>10
please show step by step
Answers:
PROBLEM 1:
|(2/3)x-4| + 20 < 10
subtract "20" from both sides... like this...
[ |(2/3)x-4| + 20] - 20 < 10 - 20
combine like terms. and you get...
|(2/3)x-4| < -10
There is no solution to this problem since the absolute value of (2/3)x-4 . or anything for that matter cannot be LESS THAN a negative number. Absolute value of ANYTHING always equals a positive number. and Positive numbers are ALWAYS larger than negative numbers, not smaller.
PROBLEM 2:
3 |2x+4| -24=12
add "24" to both sides...
( 3 |2x+4| - 24 ) + 24 = 12 + 24
combine like terms...
3 |2x+4| = 36
divide both sides by 3
|2x+4| = 12
2x + 4 = 12 . 2x = 8. x = 4
-(2x+4) = 12 . 2x+4 = -12 ... 2x = -16 . x = -8
So... the solution is "x = 4"... and "x = -8"
LAST PROBLEM:
x< -2 or x > 10 has to make the inequality true.
The inequality can be either.
|4-x| + 4 > 10
OR
|4-x| > 6
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