Solving Multi-Step Equations by Adding/Removing Same Values
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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:

<p>Add/Subtract the same value = The equation's balance is maintained Combine like terms = Similar expressions are merged Isolate the variable = The variable is rewritten as the subject Check the equation's sign = Negative numbers can change the equation's sign</p> Signup and view all the answers

Match the following equation solving steps with their importance:

<p>Identify the equation and variable = Crucial for understanding the problem Determine the value to add/remove = Essential for isolating the variable Perform the operation on both sides = Critical for maintaining the equation's balance Simplify the equation = Important for presenting the solution clearly</p> Signup and view all the answers

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:

  1. Identify the equation and the variable you want to isolate.
  2. Determine the value that needs to be added or removed from both sides of the equation.
  3. Add or subtract the value from both sides of the equation.
  4. 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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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.

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