12 Questions
What is the goal of solving linear equations in one variable?
To find the value of the variable that satisfies the given equation
In the equation X + 7 = 12, what is the first step to solve for X?
Transposing 7 to the other side of the equation, changing its sign to negative
What is the value of X in the equation 2X + 3 = 9?
X = 3
In the equation 3(X + 2) = 2, what is the first step to solve for X?
Using the distributive property to multiply 3 with the terms inside the parenthesis
What is the value of X in the equation (2X - 3)/6 = X + 4?
X = -27/4
What is the purpose of cross-multiplication in the equation (2X - 3)/6 = X + 4?
To eliminate the denominator
What is represented by the two bars, | |?
The distance of a number from zero on the number line
What is the absolute value of the number -5?
5
What is the absolute value of the expression |-8| + 10?
18
What is the absolute value of the expression |-15| - |-3|?
12
What is the purpose of finding the absolute value of a number?
To find the distance of a number from zero on the number line
What is the absolute value of the expression |14| + |-6|?
20
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
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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.
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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.
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.
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