Question

solve the inequality and graph the solution.
\\(\frac{a}{2} < 2\\)
plot the endpoints. select an endpoint to change it from closed to open. select the middle of the segment, ray, or line to delete it.
submit

Explanation:

Step1: Multiply both sides by 2

To solve the inequality \(\frac{a}{2} < 2\), we multiply both sides of the inequality by 2 to isolate \(a\). When we multiply both sides of an inequality by a positive number, the direction of the inequality sign remains the same. So we have:

$$ \frac{a}{2} \times 2 < 2\times 2 $$

Step2: Simplify both sides

Simplifying the left - hand side, \(\frac{a}{2}\times2=a\), and simplifying the right - hand side, \(2\times2 = 4\). So the solution to the inequality is \(a < 4\)? Wait, no, wait. Wait, the original inequality is \(\frac{a}{2}<2\). Let's do it again. Multiply both sides by 2: \(\frac{a}{2}\times2<2\times2\), which gives \(a < 4\)? No, wait, 2 times 2 is 4? Wait, no, the original inequality is \(\frac{a}{2}<2\). So multiplying both sides by 2: \(a < 2\times2=4\)? Wait, no, that's a mistake. Wait, \(\frac{a}{2}<2\), multiply both sides by 2: \(a < 4\)? Wait, no, let's check with an example. If \(a = 3\), \(\frac{3}{2}=1.5<2\), which works. If \(a = 4\), \(\frac{4}{2}=2\), which is not less than 2. If \(a = 5\), \(\frac{5}{2}=2.5>2\). Wait, but the number line has numbers from - 5 to 5. Wait, maybe I misread the inequality. Wait, the inequality is \(\frac{a}{2}<2\)? Wait, no, maybe it's \(\frac{a}{2}<2\), but let's solve it correctly.

Wait, let's start over. The inequality is \(\frac{a}{2}<2\). To solve for \(a\), we multiply both sides by 2 (since 2 is positive, the inequality sign direction doesn't change):

\(\frac{a}{2}\times2<2\times2\)

\(a < 4\)? Wait, no, 2 times 2 is 4? Wait, no, \(\frac{a}{2}<2\) implies \(a < 4\)? Wait, but let's check with \(a = 3\), \(\frac{3}{2}=1.5 < 2\), correct. \(a = 4\), \(\frac{4}{2}=2\), not less than 2. \(a = 5\), \(\frac{5}{2}=2.5>2\). So the solution is \(a < 4\)? But the number line is from - 5 to 5. Wait, maybe the inequality is \(\frac{a}{2}<2\), so the solution is all real numbers less than 4. To graph this, we draw an open circle at 4 (because the inequality is strict, \(a < 4\), not \(a\leq4\)) and draw a ray to the left of 4.

Wait, but maybe I made a mistake. Let's check the inequality again. The user wrote \(\frac{a}{2}<2\). So solving it:

Multiply both sides by 2: \(a < 4\). So the solution is \(a\in(-\infty,4)\).

Answer:

The solution to the inequality \(\frac{a}{2}<2\) is \(a < 4\). To graph the solution, place an open circle at \(a = 4\) on the number line and draw a ray extending to the left from 4 (indicating all values of \(a\) less than 4).