Question

inequalities vs. equations
what does it mean to solve an inequality?
why are there millions of solutions?
what would the solution look like?
is 8 a solution?
½(?) + 2 ≤ 8
? ≤ 6 because it is? then it is is not a solution

Explanation:

Step1: Define solving an inequality

Solving an inequality means finding all values of the variable that make the inequality true. Since inequalities represent a range of values rather than a single - point solution like equations, there can be infinitely many (millions in some cases) values that satisfy the inequality.

Step2: Analyze the given inequality

We have the inequality $\frac{1}{2}x + 2\leq6$. First, we solve it for $x$.
Subtract 2 from both sides: $\frac{1}{2}x+2 - 2\leq6 - 2$, which simplifies to $\frac{1}{2}x\leq4$.
Then multiply both sides by 2 to isolate $x$: $x\leq8$.

Step3: Check if 8 is a solution

Since the inequality is $x\leq8$, when $x = 8$, $\frac{1}{2}(8)+2=4 + 2=6$, and $6\leq6$ is True. So 8 is a solution.

Answer:

8 is a solution of the inequality $\frac{1}{2}x + 2\leq6$.