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Writing an Equation

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[MUSIC PLAYING] Let's look at our objectives for today. We'll start by reviewing how to solve an equation. We'll then discuss the crucial steps for representing situations as equations. Finally, we'll do some examples creating an equation from a situation.

Let's review how to solve an equation. An equation is a mathematical statement that two expressions are equal or have the same value. When solving an equation, we want to determine or solve for the value of the variable or the unknown quantity. The first step in solving an equation is to combine like terms on either side of the equation. We can then use inverse operations to undo operations in the equation to isolate the variable.

Now, let's go over the crucial steps in representing a situation with an equation. First, avoid skimming the problem. And instead, read the entire problem to avoid missing or misinterpreting any information. Then determine what the question is asking you to find. These unknown quantities will help identify and define the variables in the equation.

Next, clearly state the letter that will be used for the variable and what that variable represents in the context of the problem. x is commonly used as a variable, but any letter or symbol can be used to represent an unknown quantity. Use the variables and other necessary given quantities from the situation to write an equation that represents the problem. And finally, review the equation to make sure it is logical and accurate.

Now, let's look at two examples of creating an equation from a For his cellular phone service, Seylon pays $32 a month plus $0.75 for each minute over the allowed minutes in her plan. Seylon received a bill for $47 last month. How many minutes did she use her phone beyond the allowed minutes?

We want to know how many minutes she used over the allowed minutes, so this will be our variable. So we define x as the number of minutes used over her allowance. Using the given information and a variable, we know that Seylon pays $32 per month plus an additional $0.75-- or 0.75 dollars-- for every minute used over the allowance.

So we'll need to multiply 0.75 times our variable, x. So 32 plus 0.75x will equal the total amount paid, $47. So our equation is 32 plus 0.75x equals 47.

To solve this equation, we want to isolate our x variable. So we'll start by subtracting 32 on both sides of the equation. This gives us 0.75x equals 15.

We'll then divide by 0.75 on both sides of the equation, which will give us x equals 20. This means that Seylon used 20 minutes over her allowance, which seems reasonable. It's not a negative number or an extravagantly big number.

We can verify that this is correct by substituting it back into the original equation. Doing this gives us 32 plus 0.75 times 20 equals 47. Simplifying the left side of the equation, we start by multiplying 0.75 times 20, which is 15. So we have 32 plus 15 equals 47.

Adding, 32 plus 15 gives us 47. So we have 47 equals 47. This is a true statement, which means our solution of x equals 20 is correct.

Let's look at our second and last example. In 2003, the population of Zimbabwe was about 12.6 million, which was 1 million more than four times the population in 1950. What was the population of Zimbabwe in 1950?

We want to find the population in 1950, so that will be our variable. So we let x equal the population of Zimbabwe in 1950, and we define this in millions of people, which will make our equation simpler to write. Using our given information, we know that the population was 12.6 million in 2003, which was 1 million more than four times the population in 1950.

So we start by multiplying four by our variable x. It is four times more than the population in 1950, which is our variable x. And 12.6 is 1 million more than 4 times x, so that means that 4x plus 1 is equal to 12.6. Therefore, our equation is 4x plus 1 equals 12.6.

To solve this equation and isolate the x variable, we start by subtracting 1 on both sides. This gives us 4x equals 11.6. We then divide by 4 on both sides of the equation, which gives us x equals 2.9. This means that the population of Zimbabwe was 2.9 million in 1950, and this, again, seems reasonable. It's not too big or small compared to 12.6 million, and the answer is not negative.

We can also verify that the solution is correct by substituting it back into our original equation. This would give us 4 times 2.9 plus 1 equals 12.6. Simplifying, we start by multiplying 4 times 2.9 equals 11.6, so we have 11.6 plus 1 equals 12.6. Adding on the left side gives us 12.6 equals 12.6, which is a true statement, which means our solution is correct.

Let's review our important points from today. Make sure you get these in your notes so you can refer to them later. Here are the crucial steps when writing an equation from a situation. First, avoid skimming. And instead, read the entire problem to avoid missing or misinterpreting any information.

Next, determine what the question is asking you to find. These unknown quantities will help identify and define the variables in the equation. Then clearly state the letter that will be used for the variable and what that variable represents in the context of the problem. x is commonly used as a variable, but any letter or symbol can be used to represent an unknown quantity. Then use the variables and other necessary given information to write an equation that represents the problem. Finally, review the equation to make sure it is logical and accurate.

So I hope that these important points and examples helped you understand a little bit more about writing an equation. Keep using your notes, and keep on practicing. And soon, you'll be a pro. Thanks for watching.