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Video: Writing and Solving One-Step Linear Inequalities for a Real-World Context

Bethani Gasparine

Joseph promised to raise at least $200 for an orphanage, so he is selling magazine subscriptions for $20 each. Write and solve an inequality that can be used to find the number of magazine subscriptions he needs to sell.

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Video Transcript

Joseph promised to raise at least two hundred dollars for an orphanage. So he is selling magazine subscriptions for twenty dollars each. Write and solve an inequality that can be used to find the number of magazine subscriptions he needs to sell.

Let’s let π‘₯ equal the number of magazine subscriptions. So if they cost twenty dollars each, we need to take twenty times π‘₯. Twenty dollars times a number of magazine subscriptions he sells will tell us the amount that he raised, and the amount that he would like to raise is at least two hundred.

So he would like to sell at least two hundred, meaning exactly two hundred dollars or more than two hundred dollars, which would be fantastic. So in order to solve this inequality, we need to divide both sides by twenty.

On the left, the twenties cancel. And on the right, two hundred divided by twenty is ten. This means that Joseph needs to sell at least ten magazine subscriptions for him to be able to reach his goal of two hundred dollars.

Again the inequality to represent this situation would be twenty π‘₯ is greater than or equal to two hundred, and solving this inequality would result in π‘₯ is greater than or equal to ten.