Problem 12 Solve. $$ 5 x-4-\quad V=4 ... [FREE SOLUTION]

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Elementary Algebra

John Redden

$Math Studyset 91影视 Explanations$ Math

2011 Edition

Chapter 8: Problem 12

Solve. $$ 5 x-4-\quad V=4 $$

Short Answer

Expert verified

$ x = \frac{V + 4}{5} $

Step by step solution

Isolate the Variable

To solve the equation $ 5x - 4 = V $, we first need to make $ x $ the subject by isolating it on one side of the equation. We start by eliminating the constant term on the left side of the equation. Add $ 4 $ to both sides to get $ 5x = V + 4 $.

Solve for x

With $ 5x = V + 4 $, we now need to solve for $ x $. Divide every term by $ 5 $ to isolate $ x $, which gives us $ x = \frac{V + 4}{5} $.

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Key Concepts

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

Isolating Variables

One foundational concept when solving equations is isolating the variable. This means getting the variable you want to solve for alone on one side of the equation. To do this, we often perform operations on both sides of the equation.
For example, in the equation $ 5x - 4 = V $, our goal is to isolate $ x $. This involves undoing what has been done to $ x $.

Start by examining the equation and identifying the terms attached to $ x $.
In this case, $ x $ is multiplied by 5 and has 4 subtracted from it.
Reverse these operations by first adding $ 4 $ to both sides to eliminate the constant, $ -4 $, yielding $ 5x = V + 4 $.

This step of adding 4 to both sides is key: equations must maintain balance, so whatever you do to one side, you do to the other.

Linear Equations

Linear equations are equations where the variable is raised to the first power, meaning it does not appear in square or higher powers. These equations often take the form $ ax + b = c $.
In the given problem, the equation $ 5x - 4 = V $ is linear.

Linear equations can be solved using straightforward operations such as addition, subtraction, multiplication, and division.
They graph as straight lines and represent a constant rate of change.

The simplicity of linear equations makes them excellent stepping stones to understanding more complex types of algebraic equations.

Algebraic Manipulation

Algebraic manipulation involves using algebraic rules to simplify expressions and solve equations. Essential operations in this process include addition, subtraction, multiplication, and division.
For our equation $ 5x = V + 4 $, algebraic manipulation comes into play as we need to isolate $ x $.

First, identify what needs to be removed to get $ x $ by itself. Here, $ x $ is multiplied by 5.
Apply division to both sides to counteract this multiplication, resulting in $ x = \frac{V + 4}{5} $.

Remember, every manipulation done to one side of the equation must also be done to the other side to maintain equivalency. Mastering these manipulations is key to solving and rearranging algebraic equations effectively.

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91影视

Solve. $$ 5 x-4-\quad V=4 $$

Short Answer

Step by step solution

Isolate the Variable

Solve for x

Key Concepts

Isolating Variables

Linear Equations

Algebraic Manipulation

One App. One Place for Learning.

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