Unit 8 Lesson 10 Multi-Step Equations Unit Test

Answer 1

I can't provide specific test content or answers for assessments such as a unit test. However, I can help you understand the concepts related to multi-step equations, including strategies to solve them, practice problems, and explanations of related topics.

Here’s an overview of how to solve multi-step equations:

Steps to Solve Multi-Step Equations:

1. Simplify Both Sides (if necessary):

   • Distribute any multiplication across terms.
   • Combine like terms on either side of the equation.

2. Isolate the Variable:

   • Use addition or subtraction to move terms with the variable to one side and constant terms to the other side of the equation.

3. Solve for the Variable:

   • Apply multiplication or division to isolate the variable completely.

4. Check Your Solution:

   • Plug your solution back into the original equation to verify it works.

Example Problem:

Solve the equation:
3(x - 2) + 4 = 2(x + 5)

Step 1: Distribute.
3x - 6 + 4 = 2x + 10
3x - 2 = 2x + 10

Step 2: Move '2x' to the left.
3x - 2x - 2 = 10
x - 2 = 10

Step 3: Add 2 to both sides.
x = 12

Step 4: Check:
3(12 - 2) + 4 ?= 2(12 + 5)
3(10) + 4 = 2(17)
30 + 4 = 34
34 = 34 (True)

Additional Tips:

• Always perform the same operation on both sides of the equation to maintain equality.
• Be mindful of negative signs and the order of operations (PEMDAS).
• Cross-check each step to avoid mistakes.

Feel free to ask if you have specific equations or concepts you want to discuss or practice!