Solving the Equation 32 - x - 1 3x - 5

Mathematics often presents us with linear equations that require some algebraic manipulation to solve. One such equation is?32 - x - 1 3x - 5. This article will guide you through the process of solving this equation and understanding the key steps involved.

Step 1: Simplify the Left Side of the Equation

The first step is to simplify the left side of the equation by combining like terms:

32 - x - 1 3x - 5

31 - x 3x - 5

Here, we have simplified the left side by combining the constant terms 32 and -1 to get 31.

Step 2: Combine Like Terms

Next, we need to consolidate all the x terms on one side of the equation and the constant terms on the other side. Let's move the -3x from the right side to the left side:

31 - x - 3x -5

31 - 4x -5

By doing this, we now have all the x terms on the left side and all the constant terms on the right side.

Step 3: Isolate the Variable

The next step is to isolate the variable x by moving the constant term on the left side to the right side:

-4x -5 - 31

-4x -36

-4x / -4 -36 / -4

x 9

By dividing both sides by -4, we get x 9. This is the solution to the equation.

Conclusion

Thus, the value of x that satisfies the equation 32 - x - 1 3x - 5 is 9. This solution can be double-checked by substituting x 9 back into the original equation:

32 - 9 - 1 3(9) - 5

32 - 10 27 - 5

22 22

As we can see, both sides of the equation are equal, confirming that x 9 is indeed the correct solution.

Additional Examples

Here are a couple of additional examples to further solidify the concept:

32 - x - 1 3x - 5

31 - x 3x - 5

4x 36

x 9

32 - 15 3x

17 3x

3x 36

x 9

32 - x - 1 3x - 5

31 - x 3x - 5

3x 31 5

3x 36

x 36 / 4

x 9

These examples further reinforce the solving approach we discussed earlier.

Understanding and solving such equations is crucial for many areas of mathematics and real-world applications. If you have any further questions or need additional examples, feel free to reach out!