Question

solve for a and graph the solution.
\\( \frac { 3 a - 2 } { 4 } > 4 \\) or \\( \frac { 5 a - 3 } { 3 } < 4 \\)
plot the endpoints. select an endpoint to change it from closed to open. select the middle of
a segment, ray, or line to delete it.

Explanation:

Step1: Solve the first inequality

Multiply both sides of \(\frac{3n - 2}{4}>4\) by \(4\): \(3n-2>16\).
Add \(2\) to both sides: \(3n>18\).
Divide both sides by \(3\): \(n > 6\).

Step2: Solve the second inequality

Multiply both sides of \(\frac{5n - 3}{3}<4\) by \(3\): \(5n-3 < 12\).
Add \(3\) to both sides: \(5n<15\).
Divide both sides by \(5\): \(n<3\).

Answer:

The solution is \(n < 3\) or \(n>6\). On the number - line, we have an open circle at \(n = 3\) (since \(n\) is not equal to \(3\)) and the line extends to the left of \(3\), and an open circle at \(n = 6\) (since \(n\) is not equal to \(6\)) and the line extends to the right of \(6\).