Question : If $4(x+5)-3>6-4x\geq x-5$, then the value of $x$ is:
Option 1: –2
Option 2: –1
Option 3: 3
Option 4: 4
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Correct Answer: –1
Solution :
To solve the compound inequality $4(x+5)–3 > 6 –4x \geq x – 5$
Solving each inequality one by one,
$4(x+5) - 3 > 6- 4x$
$⇒4x + 20 -3 > 6 - 4x$
$⇒4x + 17 > 6- 4x$
$⇒8x + 17 > 6$
$⇒x > \frac{–11}{8}$
So, the solution to the first inequality is $x > \frac{–11}{8}$.
Also, \(6 -4x \geq x - 5\)
$⇒6 \geq 5x -5$
$⇒11 \geq 5x$
$⇒\frac{11}{5} \geq x$
So, the values of $x$ that satisfy the original compound inequality are in the range: $\frac{–11}{8} < x \leq \frac{11}{5} = –1.375 < x \leq 2.2$
So, the value of $x$ is –1.
Hence, the correct answer is –1.
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