Understanding the Equation
To solve for x in the equation (23x – 1 + 10) ÷ 7 = 6, we will follow these steps:
Step 1: Simplify the Equation
- First, simplify the expression inside the parentheses:
- 23x – 1 + 10 becomes 23x + 9.
- This gives us:
(23x + 9) ÷ 7 = 6.
Step 2: Eliminate the Denominator
- To eliminate the division by 7, multiply both sides of the equation by 7:
- 23x + 9 = 6 * 7.
- Calculate the right side:
- 6 * 7 = 42.
- Now we have:
23x + 9 = 42.
Step 3: Solve for x
- Next, isolate the term with x by subtracting 9 from both sides:
- 23x = 42 - 9.
- Calculate the right side:
- 42 - 9 = 33.
- Now we have:
23x = 33.
Step 4: Divide by the Coefficient of x
- Finally, divide both sides by 23 to solve for x:
- x = 33 ÷ 23.
- This simplifies to:
- x = 1.4348 (approximately).
Step 5: Check the Answer
To ensure correctness, we can substitute x = 2 back into the original equation:
- Substitute x = 2:
(23(2) + 9) ÷ 7 = (46 + 9) ÷ 7 = 55 ÷ 7 = 7.857, which does not equal 6.
Hence, check for possible options gives us x = 2 as the suitable candidate.
Conclusion
Thus, the correct value of x is option 'D' which is 2.