When you're solving linear equations, one important step is isolating the variable. This means you want to rearrange the equation so that the variable is all by itself on one side.
Here’s a simple guide to help you learn this, especially using multiplication and division.
Start with the Equation: Begin with a simple linear equation, like
3x = 12.
Understand the Operation: In this equation, the variable x is multiplied by 3. To get x alone, we need to do the opposite of multiplication.
Use Division: Since x is multiplied by 3, we will divide both sides of the equation by 3: x = 12 ÷ 3.
Simplify: Doing the division gives: x = 4. Great! Now x is isolated.
Let’s look at a slightly harder equation:
4x + 8 = 32.
Subtract First: To get 4x alone, first subtract 8 from both sides:
4x = 32 - 8,
which simplifies to
4x = 24.
Now Divide: Next, divide both sides by 4: x = 24 ÷ 4.
Final Result: Simplifying gives us: x = 6.
Use Opposite Operations: Always remember to perform the opposite operation. If you divided to isolate x, then you should multiply in a different problem.
Keep It Balanced: Whatever change you make to one side of the equation, do the same to the other side to keep it balanced.
Check Your Answer: Put your answer back into the original equation to make sure it works.
By following these steps, you’ll feel more confident when solving different linear equations!
When you're solving linear equations, one important step is isolating the variable. This means you want to rearrange the equation so that the variable is all by itself on one side.
Here’s a simple guide to help you learn this, especially using multiplication and division.
Start with the Equation: Begin with a simple linear equation, like
3x = 12.
Understand the Operation: In this equation, the variable x is multiplied by 3. To get x alone, we need to do the opposite of multiplication.
Use Division: Since x is multiplied by 3, we will divide both sides of the equation by 3: x = 12 ÷ 3.
Simplify: Doing the division gives: x = 4. Great! Now x is isolated.
Let’s look at a slightly harder equation:
4x + 8 = 32.
Subtract First: To get 4x alone, first subtract 8 from both sides:
4x = 32 - 8,
which simplifies to
4x = 24.
Now Divide: Next, divide both sides by 4: x = 24 ÷ 4.
Final Result: Simplifying gives us: x = 6.
Use Opposite Operations: Always remember to perform the opposite operation. If you divided to isolate x, then you should multiply in a different problem.
Keep It Balanced: Whatever change you make to one side of the equation, do the same to the other side to keep it balanced.
Check Your Answer: Put your answer back into the original equation to make sure it works.
By following these steps, you’ll feel more confident when solving different linear equations!