Find the range of the value of x satisfying the inequalities 5 + x \(\leq\) 8 and 13 + x \(\geq\) 7

  • A -3 \(\leq\) x \(\leq\) 3
  • B 3 \(\leq\) x \(\leq\) 6
  • C -6 \(\leq\) x \(\leq\) 3
  • D -6 \(\leq\) x \(\leq\) -3
jamb 2003mathematics

The correct answer is C. -6 \(\leq\) x \(\leq\) 3

Let's solve each inequality separately and then find the common range of values that satisfy both inequalities.

1. \(5 + x \leq 8\):

Subtract 5 from both sides:

\(x \leq 3\).

2. \(13 + x \geq 7\):

Subtract 13 from both sides:

\(x \geq -6\).

Now, let's find the common range of values that satisfy both inequalities:

The values of \(x\) that satisfy both \(x \leq 3\) and \(x \geq -6\) are in the range \(-6 \leq x \leq 3\).

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