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Chapter 2: Problem 5

Solve each equation, and check your solution. $$ x-3=9 $$

Short Answer

Expert verified
The solution is \( x = 12 \).

Step by step solution

01

Isolate the Variable

To isolate the variable, add 3 to both sides of the equation:\[ x - 3 + 3 = 9 + 3 \]
02

Simplify Both Sides

Simplify the equation to get:\[ x = 12 \]
03

Check the Solution

Substitute 12 back into the original equation to verify the solution:\[ 12 - 3 = 9 \]This confirms that our solution is correct.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Isolate the Variable
One of the first steps to solving a linear equation is to isolate the variable. This means moving the variable to one side of the equation, separate from the constants. In our example, the equation is \( x - 3 = 9 \). To isolate the variable \( x \), you need to get rid of the \( -3 \) on the left side.
You can do this by performing the opposite operation to both sides of the equation.
  • In this case, since \( -3 \) is subtracted from \( x \), you will add 3 to both sides.
Now the equation looks like this: \[ x - 3 + 3 = 9 + 3 \].
This step ensures that you have \( x \) by itself on one side of the equation.
Simplify the Equation
Once you have isolated the variable, the next step is to simplify the equation. Simplifying means performing the operations you indicated.
  • In this case, after adding 3 to both sides, you combine like terms.
Your equation \[ x - 3 + 3 = 9 + 3 \] simplifies to \[ x = 12 \] This is because \( -3 \) and \( +3 \) cancel out to 0, leaving just \( x \) on the left side.
And \[ 9 + 3 \] simplifies to \[ 12 \] on the right side.
Congratulations! You have now found the value of \( x \).
Check the Solution
The final step in solving a linear equation is to check your solution. This ensures that your solution is correct.
In our example, the solution we found is \( x = 12 \). To check the solution:
  • Substitute \( x \) back into the original equation.
The original equation is \[ x - 3 = 9 \] After substituting \( x = 12 \), you get \[ 12 - 3 = 9 \]
Simplifying the left side: \[ 12 - 3 = 9 \] This simplifies to \[ 9 = 9 \], which is a true statement.
This confirms that our solution \( x = 12 \) is correct!

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Most popular questions from this chapter

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