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The Correct Answer and Explanation is:
The equation in the image is:
Given equation: x+2=5x + 2 = 5
Step-by-step solution:
- Subtract 2 from both sides
To isolate xx, subtract 2 from both sides of the equation: x+2−2=5−2x + 2 – 2 = 5 – 2 - Simplify both sides
On the left-hand side, +2−2=0+2 – 2 = 0, so it simplifies to just xx.
On the right-hand side, 5−2=35 – 2 = 3. x=3x = 3
Explanation
Solving equations is a fundamental concept in algebra. The goal is to find the value of the unknown variable, in this case, xx. The given equation is a simple linear equation: x+2=5x + 2 = 5
This means that when 2 is added to some number xx, the result is 5. To find out what xx must be, we use the principle of equality: whatever operation we do to one side of the equation, we must also do to the other side to keep the equation balanced.
Here, we want to isolate xx, which means getting it alone on one side of the equation. Since 2 is being added to xx, the inverse operation is subtraction. So, we subtract 2 from both sides: x+2−2=5−2x + 2 – 2 = 5 – 2
This step simplifies the left-hand side to just xx because +2−2=0+2 – 2 = 0. On the right-hand side, 5−25 – 2 simplifies to 3. Thus, we are left with: x=3x = 3
This is the solution to the equation. We can check our answer by substituting it back into the original equation: 3+2=53 + 2 = 5
This is true, so our solution is correct. This method can be applied to any simple linear equation where a number is added or subtracted from the variable. It’s a core algebraic skill that forms the basis for solving more complex equations later on.
