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Chapter 5: Problem 81

Review factoring expressions and solving equations. $$ 3 x-1=0 $$

Short Answer

Expert verified
x = \frac{1}{3}

Step by step solution

01

Move constant to the other side

Add 1 to both sides of the equation to isolate the term containing the variable. \( 3x - 1 + 1 = 0 + 1 \) This simplifies to: \( 3x = 1 \)
02

Solve for the variable

Divide both sides of the equation by 3 to solve for x. \( \frac{3x}{3} = \frac{1}{3} \) This simplifies to: \( x = \frac{1}{3} \)

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Key Concepts

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

Factoring Expressions
Before we even start working on solving equations, we need to understand factoring expressions. Factoring is the process of breaking down an expression into simpler parts called factors. It helps simplify expressions and solve equations more easily.
Isolating Variables
Isolating variables is a crucial step when solving linear equations. It involves manipulating the equation to get the variable by itself on one side of the equation. Steps to isolate the variable:
  • First, move any constants (numbers without variables) to the other side of the equation.
  • Use addition or subtraction to achieve this.
    • Example: In the equation, 3x鈭�1=0, we add 1 to both sides to isolate the term with the variable: 3x-1+1=0+1. This simplifies to 3x=1.
Solving for x
After isolating the variable, the final step is to solve for x. Solving for x involves making the coefficient of x equal to 1. Steps to solve for x:
  • Divide both sides of the equation by the coefficient of x.
  • This step will give us the value of x.
    • Example: In the equation, 3x=1, we divide both sides by 3 to solve for x: \( \frac{ 3x }{ 3 } = \frac{ 1 }{ 3 } \). This simplifies to \( x = \frac{ 1 }{ 3 } \).

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Most popular questions from this chapter

To prepare for Section \(5.2,\) review operations with integers (Sections \(1.5-1.7)\) Perform the indicated operations. $$ -3+(-11) $$

Review factoring expressions and solving equations. $$ 4 x=0 $$

Replace \(\square\) with \(>,<,\) or \(=\) to write a true sentence. $$ 4^{3} \square 5^{3} $$

Replace \(\square\) with \(>,<,\) or \(=\) to write a true sentence. $$ 9^{7} \square 3^{13} $$

Find a value of the variable that shows that the two expressions are not equivalent. Answers may vary. $$ \frac{t^{6}}{t^{2}} ; t^{3} $$
See all solutions

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