Problem 88
Question
Solve each absolute value inequality. $$2>|11-x|$$
Step-by-Step Solution
Verified Answer
The solution to the absolute value inequality is \(9 < x < 13\).
1Step 1: Break the Absolute Value Inequality into Two Separate Inequalities
First, express the absolute value inequality as two separate inequalities: \(11-x < 2\) and \(11-x > -2\)
2Step 2: Solve Each Inequality
Now, solve each inequality separately.\nFor \(11-x < 2\), isolate \(x\): add \(x\) to both sides and subtract \(2\) from both sides to get \(x > 9\).\nFor \(11-x > -2\), isolate \(x\): add \(x\) to both sides and add \(2\) to both sides to get \(x < 13\).
3Step 3: Write as a Compound Inequality
Combine the two inequalities into a single compound inequality to denote the solution:\(9 < x < 13.\)
Other exercises in this chapter
Problem 88
Will help you prepare for the material covered in the next section. Multiply and simplify: \(12\left(\frac{x+2}{4}-\frac{x-1}{3}\right)\)
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Find all values of \(x\) satisfying the given conditions. $$ y=x-\sqrt{x-2} \text { and } y=4 $$
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Evaluate \(x^{2}-(x y-y)\) for \(x\) satisfying \(\frac{13 x-6}{4}=5 x+2\) and \(y\) satisfying \(5-y=7(y+4)+1\).
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Solve each equation in Exercises \(83-108\) by the method of your choice. $$ x^{2}-2 x=1 $$
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