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Chapter 5: Problem 304

In the following exercises, solve the equation. $$ q-0.47=-1.53 $$

Short Answer

Expert verified
q = -1.06

Step by step solution

01

Understand the equation

The provided equation is \( q - 0.47 = -1.53 \). The goal is to isolate the variable \( q \).
02

Add 0.47 to both sides

To isolate \( q \), add 0.47 to both sides of the equation:\( q - 0.47 + 0.47 = -1.53 + 0.47 \).
03

Simplify the equation

Simplify both sides of the equation:\( q = -1.06 \).

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Key Concepts

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

Isolate Variable
When solving linear equations, our goal is to isolate the variable. This means we need to get the variable by itself on one side of the equation. In the equation given, we have \( q - 0.47 = -1.53 \). To isolate \( q \), we need to remove the \( -0.47 \) from the left-hand side of the equation. Removing it involves doing the opposite operation. Hence, we use addition to cancel out the subtraction.
Addition Property of Equality
The addition property of equality states that you can add or subtract the same number to both sides of an equation without changing the equality. Here, to move the \( -0.47 \) term, we add \( 0.47 \) to both sides of the equation. This step looks like this:
\( q - 0.47 + 0.47 = -1.53 + 0.47 \).
This keeps the equation balanced while helping us isolate the variable.
Solving Negative Numbers
Dealing with negative numbers can sometimes be tricky. In our problem, after using the addition property, we have \( -1.53 + 0.47 \) on the right side.
Subtracting numbers involves adding their absolute values when both numbers are negative.
Here is how it works:
1. Find the absolute values: \( |-1.53| = 1.53 \) and \( |0.47| = 0.47 \).
2. Subtract the smaller absolute value from the larger one: \( 1.53 - 0.47 = 1.06 \).
3. Keep the sign of the number with the larger absolute value: \( -1.06 \). Therefore, \( q = -1.06 \).

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Most popular questions from this chapter

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