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Chapter 2: Problem 12

Solve each equation, and check your solution. $$ x+7=11 $$

Short Answer

Expert verified
x = 4

Step by step solution

01

- Isolate the variable

To solve for the variable x, begin by isolating it on one side of the equation. Subtract 7 from both sides of the equation: $$x + 7 - 7 = 11 - 7$$
02

- Simplify both sides

Simplify both sides of the equation: $$x = 4$$
03

- Check the solution

To verify the solution, substitute x back into the original equation: $$4 + 7 = 11.$$ Since both sides equal, our solution is correct.

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Key Concepts

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

Isolating Variables
To solve linear equations effectively, we must understand the process of isolating the variables. This means getting the variable (like x) alone on one side of the equation.

For example, in the equation \(x + 7 = 11\), we can isolate x by performing the same operation on both sides of the equation. Here, we'll subtract 7 from both sides: \[ x + 7 - 7 = 11 - 7 \]
This leaves us with \( x = 4 \). By isolating x, we've found its value.

Remember: Always perform the same operation on both sides to keep the equation balanced!
Simplifying Equations
Once we have isolated the variable, the next step is to simplify the equation. Simplifying means to perform basic arithmetic to make the equation easier to understand.

In our previous example, \(x + 7 - 7 = 11 - 7\), we simplified by subtracting 7: \[ x + 0 = 4 \]

Since adding zero doesn't change the value, we simplify to \( x = 4 \).

Keeping equations simple helps in understanding and solving them faster!
Checking Solutions
After finding the value of the variable, we must check if it's correct. To check the solution, plug the variable's value back into the original equation.

For our example, \(x = 4\), we substitute 4 in the equation \(x + 7 = 11\): \[ 4 + 7 = 11 \]

Both sides equal 11, so our solution x = 4 is correct.

Verification is essential in ensuring our answers are accurate!

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