Podcast
Questions and Answers
What is the goal of solving linear equations in one variable?
What is the goal of solving linear equations in one variable?
In the equation X + 7 = 12, what is the first step to solve for X?
In the equation X + 7 = 12, what is the first step to solve for X?
What is the value of X in the equation 2X + 3 = 9?
What is the value of X in the equation 2X + 3 = 9?
In the equation 3(X + 2) = 2, what is the first step to solve for X?
In the equation 3(X + 2) = 2, what is the first step to solve for X?
Signup and view all the answers
What is the value of X in the equation (2X - 3)/6 = X + 4?
What is the value of X in the equation (2X - 3)/6 = X + 4?
Signup and view all the answers
What is the purpose of cross-multiplication in the equation (2X - 3)/6 = X + 4?
What is the purpose of cross-multiplication in the equation (2X - 3)/6 = X + 4?
Signup and view all the answers
What is represented by the two bars, | |?
What is represented by the two bars, | |?
Signup and view all the answers
What is the absolute value of the number -5?
What is the absolute value of the number -5?
Signup and view all the answers
What is the absolute value of the expression |-8| + 10?
What is the absolute value of the expression |-8| + 10?
Signup and view all the answers
What is the absolute value of the expression |-15| - |-3|?
What is the absolute value of the expression |-15| - |-3|?
Signup and view all the answers
What is the purpose of finding the absolute value of a number?
What is the purpose of finding the absolute value of a number?
Signup and view all the answers
What is the absolute value of the expression |14| + |-6|?
What is the absolute value of the expression |14| + |-6|?
Signup and view all the answers
Study Notes
Solving Linear Equations in One Variable
- The goal is to find the value of the variable that satisfies the given equation, also known as the solution.
Example 1: X + 7 = 12
- To solve, transpose 7 to the other side of the equation, changing its sign to negative.
- Simplify the equation: 12 - 7 = 5, so the value of x is 5.
Example 2: 2X + 3 = 9
- Transpose 3 to the other side, changing its sign to negative.
- Simplify the equation: 2X = 9 - 3, which equals 2X = 6.
- Divide both sides by 2 to solve for x: x = 6 ÷ 2 = 3.
Example 3: 3(X + 2) = 2
- Use the distributive property to multiply 3 with the terms inside the parenthesis.
- Simplify the equation: 3X + 6 = 2, which equals 3X = 2 - 6.
- Divide both sides by 3 to solve for x: x = -4 ÷ 3 = -4/3.
Example 4: (2X - 3)/6 = X + 4
-
Method 1: Cross-multiplication
- Express the right side of the equation as a fraction: X + 4 = X/1 + 4/1.
- Cross-multiply: 6(X + 4) = 2X - 3.
- Simplify the equation: 6X + 24 = 2X - 3, which equals 4X = -27.
- Divide both sides by 4 to solve for x: x = -27 ÷ 4 = -27/4.
-
Method 2: Multiply the entire equation by 6 to eliminate the denominator.
- Simplify the equation: 2X - 3 = 6X + 24.
- Combine like terms: -4X = 27.
- Divide both sides by -4 to solve for x: x = -27 ÷ 4 = -27/4.
Studying That Suits You
Use AI to generate personalized quizzes and flashcards to suit your learning preferences.
Description
Learn how to solve linear equations in one variable with examples of different types of equations. Practice solving for x with step-by-step explanations.
