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Solving Linear Equations in One Variable

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Solving Linear Equations in One Variable

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Questions and Answers

What is the goal of solving linear equations in one variable?

To find the value of the variable that is always one

To find the value of the variable that is always zero

To find the value of the variable that satisfies the given equation (correct)

To find the value of the variable that does not satisfy the 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 (correct)

Transposing 7 to the other side of the equation, changing its sign to positive

Transposing 12 to the other side of the equation, changing its sign to negative

Transposing 7 to the same side of the equation

What is the value of X in the equation 2X + 3 = 9?

X = 4

X = 2

X = 3 (correct)

X = 5

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 Signup and view all the answers

What is the value of X in the equation (2X - 3)/6 = X + 4?

X = -27/4 Signup and view all the answers

What is the purpose of cross-multiplication in the equation (2X - 3)/6 = X + 4?

To eliminate the denominator Signup and view all the answers

What is represented by the two bars, | |?

The distance of a number from zero on the number line Signup and view all the answers

What is the absolute value of the number -5?

5 Signup and view all the answers

What is the absolute value of the expression |-8| + 10?

18 Signup and view all the answers

What is the absolute value of the expression |-15| - |-3|?

12 Signup and view all the answers

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 Signup and view all the answers

What is the absolute value of the expression |14| + |-6|?

20 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.

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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.