Question

select the TWO values of X that SATISFY this inequality. 3x + 4 _< 1/2 (x + 4) - 6

Answer 1

To solve the inequality \( 3x + 4 \leq \frac{1}{2} (x + 4) - 6 \), we first need to simplify the right side of the inequality.

1. Distribute \(\frac{1}{2}\) on the right side:
\[
\frac{1}{2} (x + 4) = \frac{1}{2}x + 2
\]
So, the inequality becomes:
\[
3x + 4 \leq \frac{1}{2}x + 2 - 6
\]

2. Combine like terms on the right side:
\[
2 - 6 = -4
\]
Thus, the inequality simplifies to:
\[
3x + 4 \leq \frac{1}{2}x - 4
\]

3. Now, rearrange the inequality to isolate \(x\):
\[
3x - \frac{1}{2}x \leq -4 - 4
\]
Simplifying the left side:
\[
\frac{6}{2}x - \frac{1}{2}x = \frac{5}{2}x
\]
And the right side simplifies to \(-8\):
\[
\frac{5}{2}x \leq -8
\]

4. Multiply both sides by \(\frac{2}{5}\) (note that this does not change the direction of the inequality because \(\frac{2}{5}\) is positive):
\[
x \leq -\frac{8 \cdot 2}{5} = -\frac{16}{5}
\]

So, the solution to the inequality is:
\[
x \leq -\frac{16}{5}
\]

Now that we have the solution, we can pick values of \(x\) that satisfy this inequality. Two example values could be:
- \(x = -4\) (which is less than \(-\frac{16}{5} \approx -3.2\))
- \(x = -5\) (which is also less than \(-\frac{16}{5}\))

Thus, two values of \(X\) that satisfy the inequality are:
\(-4\) and \(-5\).