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Questions and Answers
What is the first step when solving the equation 3(x - 4) = 15?
What is the first step when solving the equation 3(x - 4) = 15?
Which operation would you perform to isolate the variable in the equation 5x + 3 = 23?
Which operation would you perform to isolate the variable in the equation 5x + 3 = 23?
In the equation 2(x + 1) = 12, after applying the first operation, what is the resultant equation?
In the equation 2(x + 1) = 12, after applying the first operation, what is the resultant equation?
Which of the following represents the correct last step in solving the equation 6x = 30?
Which of the following represents the correct last step in solving the equation 6x = 30?
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When solving an equation with fractions, what is usually the first step to simplify the equation?
When solving an equation with fractions, what is usually the first step to simplify the equation?
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What can often be a source of errors when solving equations?
What can often be a source of errors when solving equations?
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If an equation has variables on both sides, which operation should you use to simplify?
If an equation has variables on both sides, which operation should you use to simplify?
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Which step follows after combining like terms in the equation 4x + 2x - 3 = 14?
Which step follows after combining like terms in the equation 4x + 2x - 3 = 14?
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Study Notes
Multi-Step Equations
- Multi-step equations require more than one step to solve for the variable.
- The goal is to isolate the variable (often 'x') on one side of the equation.
Identifying the Operations
- Addition and subtraction are inverse operations.
- To undo addition, subtract the same value from both sides.
- To undo subtraction, add the same value to both sides.
- Multiplication and division are inverse operations.
- To undo multiplication, divide both sides by the same value.
- To undo division, multiply both sides by the same value.
Steps for Solving Multi-Step Equations
- Distribute: Apply the number outside parentheses to each term inside.
- Combine Like Terms: Simplify each side by combining terms with the same variables.
- Isolate the variable term: Use addition or subtraction to move constant terms to the opposite side.
- Isolate the variable: Use multiplication or division to solve for the variable.
Examples
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Example 1: Solve 2x + 5 = 11
- Subtract 5 from both sides: 2x = 6
- Divide both sides by 2: x = 3
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Example 2: Solve 3(x - 2) = 9
- Distribute: 3x - 6 = 9
- Add 6 to both sides: 3x = 15
- Divide both sides by 3: x = 5
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Example 3: Solve 4x - 7 + 2x = 13
- Combine like terms: 6x - 7 = 13
- Add 7 to both sides: 6x = 20
- Divide both sides by 6: x = 20/6 = 10/3 (approximately 3.33)
Important Considerations
- Order of Operations (PEMDAS/BODMAS): Follow order of operations (parentheses, exponents, multiplication and division, addition and subtraction) when simplifying expressions.
- Checking your solution: Substitute your solution back into the original equation to verify it's correct.
- Variables on Both Sides: If the variable appears on both sides, move it to one side using addition or subtraction.
Different Situations
- Equations with fractions: Use common denominators to simplify.
- Word problems: Translate word problems into equations and solve.
- Equations with decimals: Pay attention to decimal places.
Practice Problems
- Solve the following equations:
- 5x - 8 = 12
- 2(x + 3) = 10
- 7x + 3 - 2x = 18
- Translate and solve: "Three times a number decreased by 4 is 11. What is the number?"
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Description
This quiz focuses on solving multi-step equations through various operations such as addition, subtraction, multiplication, and division. You will learn to identify the necessary steps including distribution and combining like terms to isolate the variable. Enhance your algebra skills with practical problems!
