Question

solve the inequality and graph the solution.
4 + 4a > -4
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.
(number line from -5 to 5 with ticks at each integer)
submit

Explanation:

Step1: Subtract 4 from both sides

To isolate the term with \(a\), we subtract 4 from both sides of the inequality \(4 + 4a > -4\). This gives us \(4 + 4a - 4 > -4 - 4\), which simplifies to \(4a > -8\).

Step2: Divide both sides by 4

To solve for \(a\), we divide both sides of the inequality \(4a > -8\) by 4. Since 4 is a positive number, the direction of the inequality sign remains the same. So we have \(\frac{4a}{4} > \frac{-8}{4}\), which simplifies to \(a > -2\).

Answer:

The solution to the inequality \(4 + 4a > -4\) is \(a > -2\). To graph this, we draw an open circle at \(-2\) (because the inequality is strict, \(>\), not \(\geq\)) and shade the line to the right of \(-2\).