How to Solve x + 2 = 5
Quick Answer
Step-by-Step Solution
Step 1: Identify the equation
x + 2 = 5
This is a linear equation in one variable (x). Our goal is to isolate x on one side of the equation.
Step 2: Subtract 2 from both sides
To isolate x, we need to remove the +2 on the left side. We do this by subtracting 2 from both sides (keeping the equation balanced):
x + 2 - 2 = 5 - 2
x = 3
Step 3: Verify the solution
Substitute x = 3 back into the original equation to verify:
3 + 2 = 5
5 = 5 ✓
The solution x = 3 is correct!
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Equation: ax + b = c
Understanding Linear Equations
What is a Linear Equation?
A linear equation is an equation that forms a straight line when graphed. It has the general form:
ax + b = c
Where:
- x is the unknown variable we're solving for
- a is the coefficient of x (cannot be zero)
- b is the constant term
- c is the result
The Golden Rule of Algebra
Whatever you do to one side of the equation, you must do to the other side.
This keeps the equation balanced and ensures your solution is correct.
Solving Strategy
- Isolate the variable term: Move all terms with x to one side
- Isolate the variable: Divide by the coefficient to solve for x
- Verify: Substitute your answer back into the original equation
More Examples
Example 1
Solve: x + 5 = 12
x = 12 - 5
x = 7
Example 2
Solve: x - 3 = 8
x = 8 + 3
x = 11
Example 3
Solve: 2x + 4 = 10
2x = 10 - 4 = 6
x = 6 / 2
x = 3
Example 4
Solve: 3x - 7 = 14
3x = 14 + 7 = 21
x = 21 / 3
x = 7
Real-World Applications
Example Problem
You have some money, and your friend gives you $2 more. Now you have $5 total. How much money did you start with?
Let x = starting amount
x + 2 = 5
x = 5 - 2 = 3
You started with $3.
Frequently Asked Questions
Why do we subtract 2 from both sides?
To solve for x, we need to isolate it. Since we have x + 2, we subtract 2 to cancel out the addition. We must do the same to both sides to keep the equation balanced.
What if the equation was x - 2 = 5?
We would add 2 to both sides instead: x - 2 + 2 = 5 + 2, giving us x = 7.
Can there be more than one solution?
For linear equations like x + 2 = 5, there is exactly one solution. This is different from quadratic equations, which can have up to two solutions.