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Chapter 5: Problem 14

Solve \(g-7.2=1.3\) for \(g\)

Short Answer

Expert verified
Answer: The value of 'g' in the given equation is 8.5.

Step by step solution

01

Add 7.2 to both sides of the equation

To isolate 'g', we need to get rid of the -7.2 on the left side of the equation. To do that, we will add 7.2 to both sides of the equation. This operation will give us the following equation: g - 7.2 + 7.2 = 1.3 + 7.2
02

Simplify the equation

After adding 7.2 to both sides, we can now simplify the equation to find the value of 'g'. The left side of the equation will result in just 'g', and the right side of the equation will be the sum of 1.3 and 7.2. The simplified equation will look like this: g = 1.3 + 7.2
03

Calculate the value of 'g'

Now, we can calculate the value of 'g'. Adding 1.3 and 7.2 on the right side of the equation will give us the value for 'g': g = 8.5 Since we have found the value of 'g', the solution to the given equation \(g-7.2=1.3\) for \(g\) is \(g=8.5\).

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Key Concepts

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

Algebraic Equations
To put it simply, an algebraic equation is a mathematical statement that shows the relationship between different quantities. It consists of algebraic expressions that are set equal to each other, and these expressions contain variables, constants, and often arithmetic operations.

The classic form of an algebraic equation involves a variable鈥攖he unknown we're solving for鈥攁nd numerical values. In the example provided, the equation is \(g - 7.2 = 1.3\), where \(g\) is the variable and 1.3 and 7.2 are constants. Understanding how to manipulate these equations is essential in not only algebra but many other areas of mathematics and science.
Isolating Variables
Isolating the variable, often the central goal in solving an equation, refers to the process of rearranging the equation so that the variable you are solving for stands alone on one side of the equation. This step is crucial because it simplifies the equation to the point where the value of the variable becomes obvious.

In the example exercise, the variable \(g\) is isolated by adding 7.2 to both sides of the equation. It is a basic principle in algebra that when you perform an operation to one side of an equation, like adding a number, you must do the same to the other side to maintain the equation's balance. This method guides you directly toward finding the value of \(g\).
Simplifying Equations
Simplifying an equation involves performing arithmetic operations to reduce the equation to its simplest form. This makes it easier to see the solution or carry out further manipulations. In our example, we initially have the equation \(g - 7.2 + 7.2 = 1.3 + 7.2\). Simplification here means carrying out the addition on both sides, which effectively eliminates the -7.2 on the left and makes way for straightforward addition on the right.

This step is less about dealing with the variable and more about handling the constants neatly. The final equation, \(g = 8.5\), is the beautifully simplified result that directly reveals the solution.

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Most popular questions from this chapter

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