Solving One-Step Inequalities by Adding or Subtracting 05:12 minutes

Video Transcript

Transcript Solving One-Step Inequalities by Adding or Subtracting

Carol is at the airport checking in for her flight. The airline has a weight limit of 50 lbs for all bags and suitcases combined. Before she puts her last bag on the scale, the scale reads 43 lbs. There's an easy way to find out if she can check her last bag – by solving one-step inequalities with addition and subtraction.

So, let's summarize our given information:

  • 43 lbs are already on the scale.
  • 50 lbs is the maximum weight limit.

This means her bags should weigh 50 lbs or less. So we use the less than or equal to sign. Now let's use this information to write an inequality.

Writing the Inequality

We want to find out how many pounds Carol can still check. Since this is an unknown value, we will represent it using a variable, for example, x.

We add this to positive 43 lbs for the bags that are already on the scale. All together, this must be less than or equal to 50 lbs.

Solving the Inequality

Now that we have written the inequality, let's solve it. There are a few things to keep in mind when solving inequalities.

  • First, remember to use opposite operations to isolate the variable.
  • Next, whatever you do to one side of the inequality must be done to the other.
  • Lastly, make sure the inequality sign stays the same.

Let's try this problem. Since 43 is added to x, you must use the opposite of addition, subtraction, to isolate x. Because you must do the same thing to both sides, you should subtract 43 from both sides of the inequality.

The +43 and the -43 will cancel out so you just have x on the left side. Then, 50 − 43 = 7. By keeping the inequality the same you get x is less than or equal to

This means Carol's last piece of luggage to check must weigh 7 lbs or less if she wants to avoid extra baggage fees.

Graphing the Inequality on a Number Line

A convenient way to show the solutions to an inequality is by graphing the answer on a number line.

x ≤ 7 means that all numbers less than or equal to 7 are solutions to this problem.

We will put a filled-in dot on the number 7 because 7 is also a solution. Then we will shade the line to the left to include all numbers less than 7.

Because the weight of the luggage can't be negative, we just need to take a look at the positive numbers on the number line.

Checking the Anwser

Now that we've solved the inequality, let's check our answer. First, we need to check the endpoint, or 7. We must plug in 7 for x and see if it makes the inequality true. Is 7 + 43 ≤ 50?

After we simplify our equation, we have 50 ≤ 50. Since 50 = 50, and plugging in 7 for x makes the inequality true, our answer is correct.

Next, you should check one more solution. Let's pick 2. Does plugging in 2 for x make the inequality true? 2 + 43 = 45. So we have 45 ≤ 50. Because this is a true statement, we know that 2 is also a solution to the inequality.

So, to solve inequalities, you can use these steps:

  • First, understand the problem. What information is given to you?
  • Then, write the inequality.
  • After that, use opposite operations to solve, then graph the inequality.
  • Finally, check the problem by plugging in the endpoint and one other solution.

Solving and Graphing Example 2

Let's solve and graph one more example. x − 25 ≥ 18.

This time we have subtraction; so in order to do the opposite, we must add 25 to both sides of the inequality.

Make sure to keep the sign facing the same way. The answer is x ≥ 43.

This time we will have an open circle on 43 because 43 is not a solution. Then we draw an arrow to the right towards all numbers that are greater than 43.

Let's get back to Carol. Unfortunately, her last piece of luggage was more than 7 lbs. No problem for Carol...