SOLUTION: 2. Let f(x) = | 7 � 3x |. Find all x for which f(x)

SOLUTION: 2. Let f(x) = | 7 � 3x |. Find all x for which f(x) > or = 10

Question 215261This question is from textbook Intermediate Algebra
: 2. Let f(x) = | 7 � 3x |. Find all x for which f(x) > or = 10 This question is from textbook Intermediate Algebra

Answer by RAY100(1637) (Show Source): You can put this solution on YOUR website!
[7-3x]>=10,,,,,,lets solve with = only,,,first
.
(7-3x) = 10,,,,,,,,,(7-3x) = -10
.
-3x = 3,,,,,,,,,,,,,,-3x = -17
.
x=-1,,,,,,,,,,,,,,,,,,x=17/3 = 5.67
.
now, plot on number line
.
,,,,,,,A,,,,,,,,,-1,,,,,,,B,,,,,,,,5.67,,,,,,C,,,,,
.
Lets check original inequality in each region
.
A,,,let x= -2,,,,13>=10,,,,, true
.
B,,,,let x=0,,,,,7>=10,,,,,not true
.
C,,,,,let x= 7,,,,,14>=10,,,,true
.
.
Therefore x<-1,,,,and x>=5.67,,,,,,-1>x>5.67,,,, answer
.
This can be done by maintaining the inequality, setting the positive absolute value as >=,,and negative as <=,,and solving, but watching the flip of inequalities as we multiply or divide by negative number, but it gets confusing, especially for this problem.
.

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