Question

1. solve and graph the solution:

$2x - 1 > 7$ or $x + 4 \leq 0$

1. solve and give the solution as a graph:

Explanation:

Step1: Solve \(2x - 1>7\)

Add 1 to both sides: \(2x-1 + 1>7 + 1\), so \(2x>8\).
Divide both sides by 2: \(\frac{2x}{2}>\frac{8}{2}\), we get \(x > 4\).

Step2: Solve \(x + 4\leq0\)

Subtract 4 from both sides: \(x+4 - 4\leq0 - 4\), so \(x\leq - 4\).

Step3: Combine the solutions

Since it's an "or" inequality, the solution is the union of the two solution sets. So the solution is \(x\leq - 4\) or \(x>4\).

(For graphing: Draw a number line. Put a closed circle at \(-4\) and shade to the left for \(x\leq - 4\). Put an open circle at \(4\) and shade to the right for \(x > 4\).)

Answer:

The solution to the inequality \(2x - 1>7\) or \(x + 4\leq0\) is \(x\leq - 4\) or \(x>4\).