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Chapter 1: Problem 35

Solve each equation. $$ y-5=20 $$

Short Answer

Expert verified
Answer: The value of y is 25.

Step by step solution

01

Write the original equation

The given equation is: $$ y-5=20 $$
02

Add 5 to both sides

To isolate y, we will add 5 to both sides of the equation: $$ y - 5 + 5 = 20 + 5 $$
03

Simplify and solve for y

Now, we simplify the equation: $$ y = 25 $$ So, the solution is y = 25.

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Key Concepts

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

Equation Solving Steps
When solving linear equations, there are a few simple steps to keep in mind. These steps will help you break down the problem and find the solution quickly. Here is a basic guideline to follow:
  • Identify the equation you need to solve, writing it down clearly.
  • Proceed to the isolation of the variable. This involves eliminating any constants that are added or subtracted from the variable.
  • Simplify the equation by performing arithmetic operations to keep one side with just the variable and constants on the other side.
  • Conclude by stating the value of the variable once you solve the equation.
Remember, practice is key to becoming proficient at solving equations. With these steps in mind, tackling equations becomes a systematic process.
Isolating Variables
Isolating the variable is a fundamental step in solving equations. It means arranging the equation such that the variable appears on its own on one side of the equation. This task might sound challenging, but it can be broken down into easier steps.
Let's consider the equation given: \( y - 5 = 20 \).
The aim is to have \( y \) all by itself on one side of the equation. To achieve this, you have to move the 5 to the opposite side of the equation.
  • Perform the opposite operation of what is currently affecting the variable. In this case, add 5 to both sides, because 5 is subtracted from \( y \).
  • The subtraction by 5 cancels out with the addition of 5, leaving you with \( y \) on one side of the equation.
This step is crucial as it leaves us with a simplified version of the equation, setting the stage for the next step.
Simplifying Equations
Once the variable is isolated, simplifying the equation means making it as straightforward as possible. The aim is to reduce the equation to a form where it's clear what the solution is.
In this case, after isolating the variable \( y \) by adding 5 to both sides, we get:
  • \( y - 5 + 5 = 20 + 5 \) turns into \( y = 25 \).
Here, both sides of the equation have been simplified. The right side sums to 25, providing the solution for \( y \). Simplification is often the last step, ensuring the equation is fully resolved. Always double-check your arithmetic here to confirm you've arrived at the correct simplification!
This process ensures clarity and accuracy, helping to avoid any potential errors in solving equations.

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Most popular questions from this chapter

In Exercises \(20-27,\) find the \(x\) value that results in \(f(x)=3\). $$ f(x)=5 x-5 $$

To determine the number of tiles needed to cover \(A\) square feet of wall, a tile layer multiplies \(A\) by the number of tiles in a square foot and then adds \(5 \%\) to the result to allow for breakage. If each tile is a square with side length 4 inches, write an expression for the number of tiles.

In Problems \(46-49\), say which of the given pair of expressions is larger. $$ 10+t^{2} \text { and } 9-t^{2} $$

Given that \(x=4\) is a solution to $$ 2 j x+z=3 $$ evaluate the expression \(16 j+2 z\).

Does the equation have a solution? Ex plain how you know without solving it. $$ 4=5+x^{2} $$
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