Question

Solve this inequality and graph the solution on a number line. Explain what
your solution means in terms of the situation.

Answer 1

To solve an inequality and graph the solution on a number line, let's look at an example:

Let's solve the inequality: 2x + 3 < 7

To solve this inequality, we'll first isolate the variable x.

2x < 7 - 3
2x < 4

Now, divide both sides of the inequality by 2:

x < 4/2
x < 2

This means that x is less than 2.

To graph this solution on a number line, draw a number line and mark a point at 2. Since x is less than 2, we use an open circle to represent 2. Then, draw an arrow to the left indicating that the numbers less than 2 are part of the solution.

So, on the number line, we have an open circle at 2 and an arrow pointing to the left. This visual representation shows us that any number less than 2 is a solution to the inequality.

In terms of the situation, this solution means that any number less than 2 will satisfy the inequality 2x + 3 < 7. For example, if x = 1, then 2(1) + 3 = 5, which is less than 7 and satisfies the inequality.