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What Are the Key Steps to Solving Word Problems with Linear Equations?

When you're faced with word problems that involve linear equations, it might seem a little tricky at first. But don't worry! We can break it down into simple steps to make it easier. Let’s look at how to solve these problems together.

Step 1: Understand the Problem

Before you start doing any math, take a moment to really read the problem. Make sure you understand what it’s asking you to find. Look for keywords that can help you figure out what to do, like “total,” “difference,” “per,” or “product.”

Example:
Imagine you have a problem that says, “A book costs 15,andanotebookcosts15, and a notebook costs 5. If you buy 3 notebooks and a certain number of books, your total spending is $75. How many books did you buy?”
Here, you need to figure out how many books you bought.

Step 2: Identify the Variables

In most word problems, you’ll need to define what the unknowns are. This is important because it helps you create your equations clearly.

Example:
In our example, let’s say:

  • xx = number of books you bought
    Now we can use xx to help us write the total cost.

Step 3: Set Up the Equation

Next, turn the words into a math equation. Use the information from the problem and the variables you defined to create that equation.

Example:
From our scenario, the total cost can be written as:
15x+5(3)=7515x + 5(3) = 75
Here, 15x15x is the cost of the xx books, and 5(3)5(3) is the cost of 3 notebooks.

Step 4: Solve the Equation

Now that you have your equation, it’s time to solve for xx. Use basic algebra to isolate xx on one side.

Example:
Keep going with our equation:
15x+15=7515x + 15 = 75
Subtract 15 from both sides:
15x=6015x = 60
Now, divide by 15:
x=4x = 4
This means you bought 4 books!

Step 5: Check Your Solution

Always double-check your work to make sure your answer fits with the problem. Plug your answer back into the original situation to see if it’s right.

Example:
If we replace xx with 4 in our total cost equation, we get:
15(4)+5(3)=60+15=7515(4) + 5(3) = 60 + 15 = 75
The total matches what was given in the problem, so we know our answer is correct.

Step 6: Write Your Conclusion

Finally, you should clearly state your answer. Many times, problems will ask you to write your answer in a complete sentence.

Example:
You might say, “I bought 4 books.”

Summary

To sum it all up, here are the six simple steps to solve word problems with linear equations:

  1. Understand the problem.
  2. Identify the variables.
  3. Set up the equation.
  4. Solve the equation.
  5. Check your solution.
  6. Write your conclusion.

By following these steps one by one, word problems with linear equations will feel a lot less scary and more manageable. Practice will make you better, so keep trying different problems, and soon you'll feel really confident in solving them!

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What Are the Key Steps to Solving Word Problems with Linear Equations?

When you're faced with word problems that involve linear equations, it might seem a little tricky at first. But don't worry! We can break it down into simple steps to make it easier. Let’s look at how to solve these problems together.

Step 1: Understand the Problem

Before you start doing any math, take a moment to really read the problem. Make sure you understand what it’s asking you to find. Look for keywords that can help you figure out what to do, like “total,” “difference,” “per,” or “product.”

Example:
Imagine you have a problem that says, “A book costs 15,andanotebookcosts15, and a notebook costs 5. If you buy 3 notebooks and a certain number of books, your total spending is $75. How many books did you buy?”
Here, you need to figure out how many books you bought.

Step 2: Identify the Variables

In most word problems, you’ll need to define what the unknowns are. This is important because it helps you create your equations clearly.

Example:
In our example, let’s say:

  • xx = number of books you bought
    Now we can use xx to help us write the total cost.

Step 3: Set Up the Equation

Next, turn the words into a math equation. Use the information from the problem and the variables you defined to create that equation.

Example:
From our scenario, the total cost can be written as:
15x+5(3)=7515x + 5(3) = 75
Here, 15x15x is the cost of the xx books, and 5(3)5(3) is the cost of 3 notebooks.

Step 4: Solve the Equation

Now that you have your equation, it’s time to solve for xx. Use basic algebra to isolate xx on one side.

Example:
Keep going with our equation:
15x+15=7515x + 15 = 75
Subtract 15 from both sides:
15x=6015x = 60
Now, divide by 15:
x=4x = 4
This means you bought 4 books!

Step 5: Check Your Solution

Always double-check your work to make sure your answer fits with the problem. Plug your answer back into the original situation to see if it’s right.

Example:
If we replace xx with 4 in our total cost equation, we get:
15(4)+5(3)=60+15=7515(4) + 5(3) = 60 + 15 = 75
The total matches what was given in the problem, so we know our answer is correct.

Step 6: Write Your Conclusion

Finally, you should clearly state your answer. Many times, problems will ask you to write your answer in a complete sentence.

Example:
You might say, “I bought 4 books.”

Summary

To sum it all up, here are the six simple steps to solve word problems with linear equations:

  1. Understand the problem.
  2. Identify the variables.
  3. Set up the equation.
  4. Solve the equation.
  5. Check your solution.
  6. Write your conclusion.

By following these steps one by one, word problems with linear equations will feel a lot less scary and more manageable. Practice will make you better, so keep trying different problems, and soon you'll feel really confident in solving them!

Related articles