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Chapter 2: Problem 20

Solve each equation using the Subtraction and Addition Properties of Equality. $$y-7.2=5$$

Short Answer

Expert verified
y=12.2

Step by step solution

01

Identify the Equation

The given equation is: y - 7.2 = 5The goal is to solve for the variable y.
02

Apply Addition Property of Equality

To isolate y, add 7.2 to both sides of the equation. This keeps the equation balanced.y - 7.2 + 7.2 = 5 + 7.2
03

Simplify Both Sides

On the left side, the -7.2 and +7.2 cancel each other out, leaving y. On the right side, add the numbers together.y = 12.2

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Key Concepts

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

Addition Property of Equality
When solving linear equations, one of the main tools we use is the Addition Property of Equality. This property tells us that we can add the same number to both sides of an equation, and the equation will still be true.
For example, in the equation \(y - 7.2 = 5\), we want to isolate the variable \(y\).
We do this by adding 7.2 to both sides of the equation:
\( y - 7.2 + 7.2 = 5 + 7.2 \)
By doing this, we ensure the equation remains balanced.
  • If you add a number to one side, make sure to add the same number to the other side.
  • It helps in getting the variable by itself on one side of the equation.
This approach is fundamental in solving linear equations accurately.
Always remember: whatever you do to one side, do the same to the other to keep the equation equal.
Isolating the variable
Isolating the variable is a crucial step in solving linear equations.
The objective is to get the variable you are solving for on one side of the equation, all by itself.
  • This usually means getting rid of other numbers or coefficients that are around the variable.
In our example, \(y - 7.2 = 5\), we want to get \(y\) by itself.
By adding 7.2 to both sides using the Addition Property of Equality, we cancel out the -7.2 on the left-hand side:
\(y - 7.2 + 7.2 = 5 + 7.2\)
This leaves us with \(y\) isolated on the left side: \(y = 12.2\).
The key here is to perform operations that will cancel out any numbers or coefficients next to the variable.
Simplification
Simplification is all about making the equation easier to work with by combining like terms and performing basic arithmetic operations.
It's an essential step when solving equations.
After using the Addition Property of Equality, we simplify both sides of our example equation:
The left side becomes just \(y\) because \(-7.2 + 7.2\) equals zero: \(y - 7.2 + 7.2 = y\).
On the right side, we add the numbers:
\(5 + 7.2 = 12.2\).
  • Combine like terms
  • Perform arithmetic operations
This leaves us with \(y = 12.2\).
Simplification makes the equation straightforward and allows us to see the solution clearly.

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Most popular questions from this chapter

Solve each inequality, graph the solution on the number line, and write the solution in interval notation. $$\frac{2}{3} y>-36$$

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Graph each inequality on the number line and write in interval notation. (a) \(\quad x \leq 5\) (b) \(\quad x \geq-1.5\) (c) \(x<-\frac{7}{3}\)

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