Question

Solve each compound inequality. Then graph the solution set.

m + 3 < 5 and m + 3 < 7
a) m < 2 and m < 4
b) m > 2 and m > 4
c) m > 2 or m < 4
d) m < 2 or m > 4

Answer 1

To solve the compound inequality m + 3 < 5 and m + 3 < 7, we find the values of m that satisfy both inequalities. The solution set is m < 2 or m > 4, and it can be graphically represented by shading the area on the number line to the left of 2 and to the right of 4.

Step-by-step explanation:

To solve the compound inequality, m + 3 < 5 and m + 3 < 7, we need to find the values of m that satisfy both inequalities. Let's solve each inequality separately:

For the first inequality, m + 3 < 5:

1. Subtract 3 from both sides: m < 2

For the second inequality, m + 3 < 7:

1. Subtract 3 from both sides: m < 4

To find the solution set for both inequalities, we need to find the values of m that satisfy both m < 2 and m < 4. This can be represented as m < 2 and m < 4.

Since m cannot be simultaneously less than 2 and greater than 4, the solution set is m < 2 or m > 4. This can be represented as m < 2 or m > 4.

Graphically, the solution set can be represented by shading the area on the number line to the left of 2 and to the right of 4.