Find thegvalues of x which satisfy the inequality \(|4-5x|\le 6\)
Correct Answer: |
B) numbers in the closed interval \(\Large \left(\frac{-2}{5},2\right) \) |
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Description for Correct answer:
\(|4-5x|\le 6\)
\(\Rightarrow 4-4x\) lies between -6 and 6
\(\Rightarrow -6\le 4-5x\le 6\)
\(\Rightarrow -6-4\le -5x\le 6-4\)
\(\Rightarrow -10\le -5x\le 2\)
\(\Rightarrow -10\ge 5x\ge -2\) by changing the sign.
\(\Rightarrow -2\le 5x\le 10\)
\(\Rightarrow -\frac{2}{5}\le x\le 2\)
that is the real numbers in the closed interval \(\Large \left(\frac{-2}{5},2\right) \) are the values of X.
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