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Chapter 8: Problem 15

In the following exercises, solve each equation. $$ y-3.8=10 $$

Short Answer

Expert verified
y = 13.8

Step by step solution

01

Identify the equation

The given equation is:y - 3.8 = 10
02

Add 3.8 to both sides

To isolate y on one side, add 3.8 to both sides of the equation:y - 3.8 + 3.8 = 10 + 3.8
03

Simplify

Simplify both sides of the equation to find the solution for y:y = 13.8

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Key Concepts

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

basic algebra
Basic algebra is a branch of mathematics that deals with symbols and the rules for manipulating those symbols. These symbols often represent numbers in equations and can be used to solve problems.
Algebra can help you solve for unknown values by performing operations like addition, subtraction, multiplication, and division.
In this exercise, we use basic algebra to solve for the unknown value of y by performing operations to isolate y on one side of the equation.
equation solving
Equation solving is the process of finding the value of an unknown variable that makes an equation true.
An equation is like a statement that says two expressions are equal, and our goal is to find a value that keeps this statement true.
For instance, in the given equation y - 3.8 = 10, we need to find the value of y that satisfies this equation.
By performing some operations, we make the equation simpler and solve for the unknown variable.
isolation method
The isolation method is a technique used in algebra to solve for a particular variable.
This involves getting the unknown variable alone on one side of the equation.
In our exercise, we isolate y to solve for it.
Here鈥檚 how we do it:
  • Start with the equation: y - 3.8 = 10
  • Add 3.8 to both sides to counteract the -3.8 and isolate the variable y: y - 3.8 + 3.8 = 10 + 3.8

Adding 3.8 to both sides cancels out the -3.8 on the left side, leaving y isolated: y = 13.8.
addition property of equality
The addition property of equality states that if you add the same number to both sides of an equation, the equality is maintained.
This is essential when solving equations because it allows us to simplify the equation without changing its meaning.
In our example, to isolate y, we add 3.8 to both sides: y - 3.8 = 10 becomes y - 3.8 + 3.8 = 10 + 3.8.
By adding 3.8 to both sides, we keep the equation balanced, ensuring that we have maintained the equality while isolating the variable y.

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Most popular questions from this chapter

In the following exercises, trach English sentence into an algebraic equation and then solve it. The sum of \(-6\) and \(m\) is 25.

In the following exercises, translate to an equation and then solve. Three less than \(y\) is \(-19\)

In the following exercises, solve each linear equation using the general strategy. $$ 6(x+6)=24 $$

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