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Chapter 11: Problem 31

Solve. $$ 8 y-35=3 y $$

Short Answer

Expert verified
y = 7

Step by step solution

01

Move variable terms to one side

Subtract 3y from both sides of the equation to get all y terms on one side: 8y - 3y - 35 = 0
02

Simplify the equation

Combine like terms to simplify the equation:5y - 35 = 0
03

Isolate the variable term

Add 35 to both sides to isolate the variable term (5y):5y = 35
04

Solve for y

Divide both sides by 5 to solve for y:y = 7

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Key Concepts

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

Variables
In algebra, variables are symbols used to represent unknown values. They are usually denoted by letters like x, y, or z. For instance, in the equation 8y - 35 = 3y, the variable is y.
When solving equations, our goal is to find the value of the variable that makes the equation true.
  • Variables can change based on the problem.
  • They allow us to form general equations and formulas.
  • In this case, 'y' can be any number that satisfies the equation.
Combining like terms
Combining like terms means simplifying algebraic expressions by adding or subtracting terms that have the same variable and exponent. In our exercise, we need to combine terms involving the variable y.

  • In the equation 8y - 35 = 3y, we first subtract 3y from both sides to get 8y - 3y - 35 = 0.
  • This reduces to 5y - 35 = 0.
  • We combined like terms (8y and -3y) to simplify the expression to 5y.
Combining like terms makes the equation simpler and easier to solve.
Isolating the variable
Isolating the variable means rearranging the equation so that the variable appears by itself on one side of the equation. This helps us to solve for the variable.

Here are the steps we used in the exercise:
  • From 5y - 35 = 0, we added 35 to both sides to get 5y = 35.
  • This step removed the constant term (-35) from the side of the variable.
By isolating y on one side, it becomes simple to find its value.
Basic algebra
Basic algebra includes understanding and manipulating algebraic expressions to solve equations. This includes operations such as addition, subtraction, multiplication, and division. Here's how we applied basic algebra in the exercise:
  • Start with the equation: 8y - 35 = 3y.
  • First, we subtracted 3y from both sides: 8y - 3y - 35 = 0.
  • This combined like terms to get: 5y - 35 = 0.
  • Then we added 35 to both sides: 5y = 35.
  • Finally, we divided both sides by 5: y = 7.
Through these operations, we found that y equals 7. These are the basic steps used in solving linear equations.

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