Question

x + 4 ≤ 5 or x + 4 > 10
choose the answer that gives both the correct solution and the correct graph.
a. solution: x ≤ 1 or x > 6
b. solution: x > 1 and x ≤ 6
c. solution: x ≥ 1 and x < 6
d. solution: x ≤ 1 or x > 6

Explanation:

Step1: Solve the first inequality

Subtract 4 from both sides of $x + 4\leq5$.
$x+4 - 4\leq5 - 4$, so $x\leq1$.

Step2: Solve the second inequality

Subtract 4 from both sides of $x + 4>10$.
$x+4 - 4>10 - 4$, so $x>6$.

Step3: Analyze the solution set and graph

The solution of the compound - inequality $x + 4\leq5$ or $x + 4>10$ is $x\leq1$ or $x>6$. The graph of $x\leq1$ has a closed circle at 1 and an arrow pointing to the left, and the graph of $x>6$ has an open circle at 6 and an arrow pointing to the right.

Answer:

A. Solution: $x\leq1$ or $x>6$; Graph: (graph with closed circle at 1, arrow to left and open circle at 6, arrow to right)