Certainly! Let's solve the inequality step by step.
Step 1: Solve the given inequality
Given:
[tex]\[ \frac{x}{2} \geq -4 \][/tex]
We need to isolate [tex]\(x\)[/tex]. To do this, multiply both sides by 2:
[tex]\[ x \geq -4 \times 2 \][/tex]
[tex]\[ x \geq -8 \][/tex]
Step 2: Given inequalities
We also have the inequalities given:
[tex]\[ x \geq -8 \][/tex]
[tex]\[ x \leq -2 \][/tex]
We need to find the values of [tex]\(x\)[/tex] that satisfy both inequalities simultaneously.
Step 3: Combine the inequalities
The combined inequality is:
[tex]\[ -8 \leq x \leq -2 \][/tex]
This combined inequality means that [tex]\(x\)[/tex] must be greater than or equal to -8 and less than or equal to -2.
Step 4: Conclusion
After considering both inequalities, the solution for [tex]\(x\)[/tex] is:
[tex]\[ -8 \leq x \leq -2 \][/tex]
In interval notation, the solution can be written as:
[tex]\[ [-8, -2] \][/tex]
This means that [tex]\(x\)[/tex] can take any value between -8 and -2, inclusive.
