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
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(7-3x) = 10,,,,,,,,,(7-3x) = -10
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-3x = 3,,,,,,,,,,,,,,-3x = -17
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x=-1,,,,,,,,,,,,,,,,,,x=17/3 = 5.67
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now, plot on number line
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,,,,,,,A,,,,,,,,,-1,,,,,,,B,,,,,,,,5.67,,,,,,C,,,,,
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Lets check original inequality in each region
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A,,,let x= -2,,,,13>=10,,,,, true
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B,,,,let x=0,,,,,7>=10,,,,,not true
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C,,,,,let x= 7,,,,,14>=10,,,,true
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Therefore x<-1,,,,and x>=5.67,,,,,,-1>x>5.67,,,, answer
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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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