Questions and Answers
Match the following multi-step equation strategies with their descriptions:
Add/Subtract the same value = Maintain the equation's balance by performing the operation on both sides Combine like terms = Simplify the equation by merging similar expressions Isolate the variable = Identify the variable and rewrite the equation to focus on it Check the equation's sign = Verify if adding or subtracting negative numbers changed the equation's sign
Match the following equation manipulation steps with their purposes:
Determine the value to add/remove = Identify the obstacle to isolate the variable Perform the operation on both sides = Maintain the equation's balance Simplify the equation = Combine like terms and rewrite the equation Verify the equation's sign = Check for possible sign changes due to negative numbers
Match the following equation examples with their solutions:
2x + 3 = 7 = 2x = 4 x - 2 = 5 = x = 7 3x - 4 = 2 = 3x = 6 x + 1 = 9 = x = 8
Match the following equation manipulation rules with their justifications:
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Match the following equation solving steps with their importance:
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Study Notes
Adding/Removing Same Values
When solving multi-step equations, one common strategy is to add or remove the same value to/from both sides of the equation. This helps to isolate the variable and simplify the equation.
Why it works:
- Adding or subtracting the same value to/from both sides of an equation does not change the equation's balance.
- This is because the same value is being added or subtracted from both sides, maintaining the equation's equality.
Key steps:
- Identify the equation and the variable you want to isolate.
- Determine the value that needs to be added or removed from both sides of the equation.
- Add or subtract the value from both sides of the equation.
- Simplify the equation by combining like terms.
Examples:
- 2x + 3 = 7
- Subtract 3 from both sides: 2x = 7 - 3
- Simplify: 2x = 4
- x - 2 = 5
- Add 2 to both sides: x = 5 + 2
- Simplify: x = 7
Important notes:
- When adding or removing values, make sure to perform the operation on both sides of the equation.
- Be careful when working with negative numbers, as adding or subtracting them can change the equation's sign.
Solving Multi-Step Equations
- Adding or subtracting the same value to/from both sides of an equation maintains the equation's balance because the same value is being added or subtracted from both sides.
- This strategy helps to isolate the variable and simplify the equation.
Key Steps to Add/Remove Same Values
- Identify the equation and the variable to be isolated.
- Determine the value that needs to be added or removed from both sides of the equation.
- Add or subtract the value from both sides of the equation.
- Simplify the equation by combining like terms.
Examples of Adding/Removing Same Values
- To solve 2x + 3 = 7, subtract 3 from both sides: 2x = 7 - 3, then simplify to 2x = 4.
- To solve x - 2 = 5, add 2 to both sides: x = 5 + 2, then simplify to x = 7.
Important Reminders
- When adding or removing values, perform the operation on both sides of the equation.
- Be cautious when working with negative numbers, as adding or subtracting them can change the equation's sign.
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Description
Learn how to add or remove the same value to/from both sides of an equation to isolate the variable and simplify the equation in multi-step equations.
