Problem 46 Solve each equation, and check y... [FREE SOLUTION]

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Beginning Algebra

Margaret L. Lial, John Hornsby

$Math Studyset 91影视 Explanations$ Math

11 Edition

Chapter 2: Problem 46

Solve each equation, and check your solution. $$ 8 z=7 z $$

Short Answer

Expert verified

z = 0

Step by step solution

- Set up the equation

The given equation is: 8z = 7z

- Isolate the variable

Subtract 7z from both sides of the equation to isolate the variable z: 8z - 7z = 7z - 7z This simplifies to: z = 0

- Check the solution

Substitute z = 0 back into the original equation to verify the solution: 8(0) = 7(0) This simplifies to: 0 = 0 The solution is correct.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Isolating Variables

Understanding how to isolate a variable is key to solving linear equations. The goal is to get the variable on one side of the equation and everything else on the other side. This helps to find the value of the variable. In the equation given, we started with:
8z = 7z

To isolate the variable z, we need to remove the same term involving z from both sides. We subtract 7z from both sides:
8z - 7z = 7z - 7z

This simplifies to:
z = 0

Now, the variable z is isolated, giving us the solution z = 0. Isolating the variable is an essential step in solving equations, as it allows us to directly determine the value of the variable.

Equation Simplification

Simplifying equations is another fundamental step in solving linear equations. Simplifying means combining like terms and reducing the equation to its simplest form. In our example:
8z = 7z

To simplify, we subtract 7z from both sides:
8z - 7z = 7z - 7z

This reduces the equation to its simplest form where we get: z = 0

Equation simplification is critical as it makes the problem easier to handle and helps clearly see the solution. Always make sure to perform the same operation on both sides of the equation to keep it balanced. This includes operations like addition, subtraction, multiplication, and division.

Verification of Solutions

After finding a solution to a linear equation, it is vital to verify that the solution is correct by substituting it back into the original equation. For the equation:
8z = 7z
and the solution z = 0, verification involves substituting 0 back into the original equation:

8(0) = 7(0)
This simplifies to:
0 = 0

The left-hand side equals the right-hand side, confirming that the solution z = 0 is correct. Verification ensures that the solution we found is truly a solution to the original equation. Always take a moment to verify your solutions to avoid mistakes and confirm your answer.

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91影视

Solve each equation, and check your solution. $$ 8 z=7 z $$

Short Answer

Step by step solution

- Set up the equation

- Isolate the variable

- Check the solution

Key Concepts

Isolating Variables

Equation Simplification

Verification of Solutions

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