Podcast
Questions and Answers
What is the primary goal when solving a linear equation?
What is the primary goal when solving a linear equation?
- To find the value of the variable that makes the equation true. (correct)
- To eliminate all constants from the equation.
- To make one side of the equation equal to zero.
- To simplify the equation by combining like terms on both sides.
In the equation $5x - 3 = 12$, which operation should be performed first to isolate the variable?
In the equation $5x - 3 = 12$, which operation should be performed first to isolate the variable?
- Subtract 5 from both sides.
- Add 3 to both sides. (correct)
- Multiply both sides by 5.
- Divide both sides by 5.
After solving a linear equation, what step should you take to confirm the solution is correct?
After solving a linear equation, what step should you take to confirm the solution is correct?
- Graph the equation on a coordinate plane.
- Compare the solution to a known constant.
- Substitute the solution back into the original equation. (correct)
- Solve the equation using a different method.
Solve this linear equation for x: $2x + 5 = 3x - 2$
Solve this linear equation for x: $2x + 5 = 3x - 2$
For the equation $\frac{x}{3} - 4 = 2$, what is the value of x?
For the equation $\frac{x}{3} - 4 = 2$, what is the value of x?
What is the next step to solve for x in the following equation? $5x + 3 = 2x - 7$
What is the next step to solve for x in the following equation? $5x + 3 = 2x - 7$
Identify the value of x that satisfies the equation: $7(x - 2) = 21$
Identify the value of x that satisfies the equation: $7(x - 2) = 21$
Solve the equation $4x - 9 = 2x + 5$ for x.
Solve the equation $4x - 9 = 2x + 5$ for x.
Flashcards
Equation
Equation
A statement that two expressions are equal, using an equal sign (=).
Variable in an Equation
Variable in an Equation
A symbol that represents an unknown value in an equation.
Solving Linear Equations
Solving Linear Equations
Finding the value of the variable that makes the equation true.
Inverse Operations
Inverse Operations
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Isolate the Variable
Isolate the Variable
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Substituting to Check Solutions
Substituting to Check Solutions
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Example of x + 5 = 15
Example of x + 5 = 15
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Example of 4x = 36
Example of 4x = 36
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Study Notes
What is an Equation?
- An equation is a statement that two expressions are equal.
- This means that both sides of the equation have the same value.
- Equations use an equal sign (=) to indicate equality.
- Equations contain a variable, which represents an unknown value.
Solving Linear Equations
- Solving a linear equation involves finding the value of the variable that makes the equation true.
- To solve for the variable, isolate it on one side of the equation.
- Use inverse operations to move terms from one side of the equation to the other.
- Addition and Subtraction:
- If a term is added to one side of the equation, subtract it from both sides to eliminate it from the original side.
- If a term is subtracted from one side of the equation, add it to both sides to eliminate it from the original side.
- Multiplication and Division:
- If a term is multiplied on one side of the equation, divide both sides by that term to eliminate it from the original side.
- If a term is divided on one side of the equation, multiply both sides by that term to eliminate it from the original side.
Examples of Solving Linear Equations
- Example 1:
- x + 5 = 15
- Subtract 5 from both sides: x + 5 - 5 = 15 - 5
- x = 10
- Example 2:
- x - 8 = 30
- Add 8 to both sides: x - 8 + 8 = 30 + 8
- x = 38
- Example 3:
- 4x = 36
- Divide both sides by 4: 4x / 4 = 36 / 4
- x = 9
- Example 4:
- x / 7 = 4
- Multiply both sides by 7: (x / 7) * 7 = 4 * 7
- x = 28
- Example 5:
- x + 1 = 10x + 10
- Combine x terms on the left side and constant terms on the right side: x - 10x = 10 - 1
- -9x = 9
- Divide both sides by -9: -9x / -9 = 9 / -9
- x = -1
- Example 6:
- 10x - 5 + 3x - 6 = 10x + 10
- Combine x terms on the left side and constant terms on the right side: 13x - 11 = 10x + 10
- 13x - 10x = 10 + 11
- 3x = 21
- Divide both sides by 3: 3x / 3 = 21 / 3
- x = 7
Substitution
- To check if the solution to a linear equation is correct, substitute the value of the variable back into the original equation.
- If both sides of the equation are equal after substitution, the solution is correct.
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