Solving Multi-Step Equations: A Guide to 2x - 3 16

Algebra is a fundamental branch of mathematics that deals with symbols and the rules for manipulating these symbols. Solving algebraic equations is a crucial part of algebra, as it helps us find the unknown values that make the equation true. This guide will walk you through the process of solving a multi-step equation using the example 2x - 3 16. We'll break down each step to ensure a clear and comprehensive understanding.

Understanding the Equation

The given equation is 2x - 3 16. This is a linear equation in one variable, x. The goal is to find the value of x that satisfies the equation.

Step 1: Isolate the Variable Term

The first step in solving this equation is to get all terms with the variable x on one side of the equation and all other terms on the other side. In this case, we want to get the term with x (2x) alone on one side of the equal sign. We can do this by adding 3 to both sides of the equation:

2x - 3 16

2x - 3 3 16 3

2x 19

Step 2: Solve for the Variable

Now that the term with x (2x) is isolated on one side, we can solve for x by dividing both sides of the equation by the coefficient of x (which is 2 in this case):

2x 19

(frac{2x}{2} frac{19}{2})

x 9.5

Step 3: Verify the Solution

To ensure that our solution is correct, we can substitute the value of x (9.5) back into the original equation to see if it satisfies the equation:

2x - 3 16

2(9.5) - 3 16

19 - 3 16

16 16

Since the equation holds true, we have correctly solved the equation and x is indeed 9.5.

Additional Examples

Let's consider a few more examples to explore the process further. These examples will help solidify your understanding of solving multi-step equations.

Example 1: 3x 4 19

3x 4 19

3x 19 - 4

3x 15

(frac{3x}{3} frac{15}{3})

x 5

Substituting x 5 back into the original equation confirms that this is the correct solution.

Example 2: 5x - 7 13

5x - 7 13

5x 13 7

5x 20

(frac{5x}{5} frac{20}{5})

x 4

Verifying the solution by substituting x 4 into the original equation:

5(4) - 7 13

20 - 7 13

13 13

Conclusion

Solving algebraic equations like 2x - 3 16 is a crucial skill for any student of mathematics. By following the three clear steps outlined in this guide, you can approach and solve these equations systematically. Whether you're a student studying for an exam or a professional looking to enhance your problem-solving skills, mastering these techniques is invaluable. Practice these steps with various equations to further cement your understanding and proficiency in solving multi-step equations.