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What Steps Should You Follow to Solve a Linear Equation in Standard Form?

Alright, let’s learn how to solve a linear equation in standard form. This form usually looks like ( ax + b = 0 ).

It's a common type of equation, and once you know the steps, you'll feel confident solving them. Here’s how to go about it:

Step 1: Understand the Standard Form

First, it’s important to know what each part of the equation means. In ( ax + b = 0 ):

  • ( a ) is the number in front of ( x ) (it can't be zero),
  • ( x ) is the letter we are trying to find, and
  • ( b ) is a constant number.

Our goal is to get ( x ) by itself.

Step 2: Rearrange the Equation

To start solving, we want to move ( b ) to the other side of the equation so that ( x ) is by itself. Here's how you can do that:

  1. Write down the equation:
    ( ax + b = 0 )
  2. Subtract ( b ) from both sides:
    ( ax = -b )

Step 3: Isolate the Variable

Now we need to isolate ( x ). Since ( a ) is multiplying ( x ), we can divide both sides by ( a ) (as long as ( a ) isn’t zero):

x=bax = \frac{-b}{a}

Step 4: Understand the Solution

Now that you have ( x ) by itself, let’s think about what that means. The fraction ( \frac{-b}{a} ) tells us the value of ( x ). This is where the line meets the x-axis if you were to draw it on a graph.

Step 5: Check Your Solution

It's always a good idea to check your answer. You can do this by putting ( x ) back into the original equation to see if it works. For example, if you found ( x ) to be a certain number, plug it back in like this:

a(ba)+b=0a\left(\frac{-b}{a}\right) + b = 0

This should simplify to ( 0 = 0 ), which means your answer is correct!

Step 6: Practice!

Finally, don’t forget that practice makes perfect! Try using different numbers for ( a ) and ( b ) to see how they change the value of ( x ). The more you practice, the easier it will become to solve linear equations.

Summary

So, when you work with a linear equation in standard form, remember to:

  1. Know what each part of the equation means.
  2. Rearrange it to isolate ( x ).
  3. Divide to find ( x ).
  4. Check your answer.
  5. Keep practicing!

This step-by-step way will help you feel more comfortable with linear equations as you move through Year 11 math. Good luck, and enjoy learning!

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What Steps Should You Follow to Solve a Linear Equation in Standard Form?

Alright, let’s learn how to solve a linear equation in standard form. This form usually looks like ( ax + b = 0 ).

It's a common type of equation, and once you know the steps, you'll feel confident solving them. Here’s how to go about it:

Step 1: Understand the Standard Form

First, it’s important to know what each part of the equation means. In ( ax + b = 0 ):

  • ( a ) is the number in front of ( x ) (it can't be zero),
  • ( x ) is the letter we are trying to find, and
  • ( b ) is a constant number.

Our goal is to get ( x ) by itself.

Step 2: Rearrange the Equation

To start solving, we want to move ( b ) to the other side of the equation so that ( x ) is by itself. Here's how you can do that:

  1. Write down the equation:
    ( ax + b = 0 )
  2. Subtract ( b ) from both sides:
    ( ax = -b )

Step 3: Isolate the Variable

Now we need to isolate ( x ). Since ( a ) is multiplying ( x ), we can divide both sides by ( a ) (as long as ( a ) isn’t zero):

x=bax = \frac{-b}{a}

Step 4: Understand the Solution

Now that you have ( x ) by itself, let’s think about what that means. The fraction ( \frac{-b}{a} ) tells us the value of ( x ). This is where the line meets the x-axis if you were to draw it on a graph.

Step 5: Check Your Solution

It's always a good idea to check your answer. You can do this by putting ( x ) back into the original equation to see if it works. For example, if you found ( x ) to be a certain number, plug it back in like this:

a(ba)+b=0a\left(\frac{-b}{a}\right) + b = 0

This should simplify to ( 0 = 0 ), which means your answer is correct!

Step 6: Practice!

Finally, don’t forget that practice makes perfect! Try using different numbers for ( a ) and ( b ) to see how they change the value of ( x ). The more you practice, the easier it will become to solve linear equations.

Summary

So, when you work with a linear equation in standard form, remember to:

  1. Know what each part of the equation means.
  2. Rearrange it to isolate ( x ).
  3. Divide to find ( x ).
  4. Check your answer.
  5. Keep practicing!

This step-by-step way will help you feel more comfortable with linear equations as you move through Year 11 math. Good luck, and enjoy learning!

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