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Chapter 2: Problem 34

\(11.8=z-3.6\)

Short Answer

Expert verified
z = 15.4

Step by step solution

01

Isolate the variable

To solve for the variable, you need to isolate it on one side of the equation. In this case, the variable is \( z \). Add \( 3.6 \) to both sides of the equation to isolate \( z \).
02

Add to both sides

Perform the addition: \( 11.8 + 3.6 = z - 3.6 + 3.6 \). This simplifies to \( 15.4 = z \).
03

Verify the solution

Substitute \( z = 15.4 \) back into the original equation to ensure it is correct: \( 11.8 = 15.4 - 3.6 \). This simplifies to \( 11.8 = 11.8 \), confirming that \( z = 15.4 \) is the correct solution.

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Key Concepts

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

Isolate the Variable
One important step in solving linear equations is to isolate the variable. The variable is the unknown value you are trying to find. To isolate the variable, you need to move all other numbers or terms to the opposite side of the equation. In our example, the equation is: 11.8 = z - 3.6The goal is to have the variable, which is \( z \), by itself on one side of the equation.

To do this, you add 3.6 to both sides. Adding the same number to both sides ensures that the equation remains balanced.

So, the equation becomes:11.8 + 3.6 = z - 3.6 + 3.6Adding 3.6 to \( -3.6 \) cancels it out, leaving:15.4 = zWith \( z \) isolated, we have found the solution.
Addition Property of Equality
The addition property of equality states that adding the same number to both sides of an equation does not change the equality. This property is essential when solving equations because it allows you to move terms around while keeping the equation balanced.

In the given example, we added 3.6 to both sides to isolate the variable \( z \).

The equation was:11.8 = z - 3.6By the addition property of equality, we added 3.6 to both sides:11.8 + 3.6 = z - 3.6 + 3.6This simplifies to:15.4 = zUsing the addition property allowed us to isolate \( z \) correctly and solve the equation efficiently.
Verification of Solutions
After finding a solution to an equation, it's essential to verify it to ensure it is correct. Verification involves substituting the solution back into the original equation and checking if both sides remain equal.

For our example, the original equation was:11.8 = z - 3.6We found that \( z = 15.4 \). To verify this solution, substitute \( z \) with 15.4 in the original equation:11.8 = 15.4 - 3.6Perform the subtraction on the right side:11.8 = 11.8Both sides of the equation are equal, confirming that the solution \( z = 15.4 \) is indeed correct. Verification helps ensure that no mistakes were made during solving, giving you confidence in your solution.

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