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Chapter 3: Problem 34

For equation, complete the solution. \(y=\frac{x}{6}-8 ;(48,\quad)\)

Short Answer

Expert verified
When \( x = 48 \), \( y = 0 \).

Step by step solution

01

Understand the Equation

The equation is given as \( y = \frac{x}{6} - 8 \). We need to find the value of \( y \) when \( x = 48 \).
02

Substitute the Value of x

Replace \( x \) in the equation with \( 48 \). Thus, the equation becomes \( y = \frac{48}{6} - 8 \).
03

Calculate the Division

Perform the division \( \frac{48}{6} \). \( \frac{48}{6} = 8 \). The equation now is \( y = 8 - 8 \).
04

Compute the Final Value

Subtract 8 from 8, which results in \( y = 0 \).

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Key Concepts

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

Algebraic Expressions
An algebraic expression is a combination of numbers, variables, and operations. In this exercise, the expression given is \( y = \frac{x}{6} - 8 \). Here, \( x \) and \( y \) are variables, and the operations involved include division and subtraction.
An algebraic expression can be evaluated by substituting numbers in place of variables. This transforms the expression into a numerical one that can be calculated. For example, substituting 48 for \( x \) in \( \frac{x}{6} \) allows us to perform the division and find the corresponding value of \( y \).
  • Variables represent unknown values and can change.
  • Operators like addition, subtraction, multiplication, and division connect variables and constants.
  • Constants are numbers without variables, like 6 and 8 in the equation.
Understanding these parts helps in simplifying and solving algebraic expressions.
Substitution Method
The substitution method is a key technique in algebra. It involves replacing a variable with its known value or expression to simplify an equation or expression. This makes calculations easier and leads to a solution.
In the given exercise, we substitute 48 for the variable \( x \) in the equation \( y = \frac{x}{6} - 8 \). This turns the algebraic expression into a straightforward arithmetic problem: \( y = \frac{48}{6} - 8 \).
  • Begin by identifying the variable you are substituting.
  • Replace the variable with its specified value.
  • Simplify the expression by following the order of operations.
This method is essential not only in solving one-variable equations but also in understanding more complex algebraic structures.
Basic Algebra
Basic algebra involves understanding and manipulating mathematical symbols and expressions to find unknown values, like solving for a variable. It lays the groundwork for more advanced mathematics and problem-solving.
In this exercise, we work through the linear equation \( y = \frac{x}{6} - 8 \). By employing basic algebraic operations like substitution and simplification, we solve for \( y \).
  • Identify the operations needed: division and subtraction in this case.
  • Perform each operation step-by-step to avoid mistakes.
  • Verify your solution by checking if each step logically follows the previous one.
Mastering these principles in basic algebra helps you build a solid foundation for tackling more complex problems, whether they involve equations with multiple variables or different types of algebraic expressions.

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Most popular questions from this chapter

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