7 is a solution to the following equation: 11 – x = 4 show how answer found
The correct answer and explanation is:
Sure! Let’s solve the equation step-by-step and then explain how the answer is found.
Given equation:
11−x=411 – x = 4
Step 1: Isolate the variable xx
To find the value of xx, we want to get xx alone on one side of the equation.
Start by subtracting 4 from both sides: 11−x=411 – x = 4
Subtract 4 from both sides: 11−x−4=4−411 – x – 4 = 4 – 4
Simplifies to: 7−x=07 – x = 0
Step 2: Move the constant to the other side
Add xx to both sides to get rid of the minus sign on xx: 7−x+x=0+x7 – x + x = 0 + x
Simplifies to: 7=x7 = x
Final answer:
x=7x = 7
Explanation:
The original equation is 11−x=411 – x = 4. The goal is to solve for xx, meaning we want to find the number that makes this equation true.
- The equation states that if you subtract some number xx from 11, the result is 4.
- To isolate xx, we first want to move all numbers to one side and xx to the other.
- Subtracting 4 from both sides of the equation helps simplify the right side to zero, making the equation easier to solve.
- This yields 7−x=07 – x = 0, which tells us that 77 minus xx equals zero.
- Adding xx to both sides removes the negative sign, giving 7=x7 = x.
- This means xx must be 7 for the original equation to hold true.
We can double-check by substituting x=7x = 7 back into the original equation: 11−7=411 – 7 = 4 4=44 = 4
Since the left side equals the right side, our solution is correct.