Tuesday - Learn & Practice: Solving Equations With a Plan
Use inverse operations, visible examples, and staged support to practice solving equations.
Quick Review
Start With the Goal
The goal of solving is to isolate the variable. We use inverse operations to "undo" what is being done to the variable.
Guided Examples
Watch the Plan Work
Example 1
Guided Example 1 (Multi-step linear)
Solve: 4(x - 2) = 12
What do I notice?
There are parentheses and a number outside being multiplied.
What am I trying to find?
The value of x.
Reasonable first step
Distribute the 4 into the parentheses.
Step-by-step solution:
4(x - 2) = 12Start
4x - 8 = 12Distribute
4x = 20Add 8 to both sides
x = 5Divide by 4
4(5 - 2) = 4(3) = 12Final check
Why it makes sense:
4(5 - 2) = 4(3) = 12. The answer balances the equation.
Example 2
Guided Example 2 (Variables on both sides)
Solve: 5x + 3 = 2x + 15
Emphasize: You can subtract 2x from both sides OR subtract 5x. Both are valid!
Solution:
Subtracting 2x keeps the variable positive.
5x + 3 = 2x + 15Start
3x + 3 = 15Subtract 2x from both sides
3x = 12Subtract 3 from both sides
x = 4Divide by 3
Practice Problems
Try Each Problem
Enter an answer, check it, and keep editing your work as you learn from feedback.
Look for terms you can combine. Then, decide which inverse operation to perform on both sides to isolate the variable. Remember to perform the same operation on both sides to keep the equation balanced.
Problem 1
x + 7 = 15
Answer: 8
Brief Explanation: Subtract 7 from both sides to isolate x: x = 8.
Problem 2
2x - 5 = 11
Answer: 8
Brief Explanation: Add 5 to both sides, then divide by 2: 2x = 16, so x = 8.
Problem 3
4(x + 1) = 12
Answer: 2
Brief Explanation: Divide both sides by 4 first or distribute and solve. Using division first: x + 1 = 3, so x = 2.
Problem 4
3x + 2 = x + 10
Hint 1: Notice variables are on both sides.
Hint 2: Subtract x from both sides to group variables.
Hint 3: Your first line should be 2x + 2 = 10.
Worked Solution:2x = 8, so x = 4.
Brief Explanation: Move the variable terms together first. Subtract x from both sides, then solve 2x + 2 = 10.
Problem 5
8 - 2x = x + 2
Hint 1: You have variables on both sides. Which side is easier to work with?
Hint 2: Add 2x to both sides.
Hint 3: Your first line should be 8 = 3x + 2.
Worked Solution:6 = 3x, so x = 2.
Brief Explanation: Adding 2x to both sides keeps the variable term positive. Then subtract 2 and divide by 3.
Problem 6
5(x - 2) = 2x + 5
Hint 1: What should you do with the parentheses first?
Hint 2: Distribute the 5, then group variables.
Hint 3: Your first line should be 5x - 10 = 2x + 5.
Worked Solution:3x = 15, so x = 5.
Brief Explanation: Distribute first, then group the variable terms on one side and constants on the other.
Tuesday Exit Check
Check What Feels Clearer Now
How many of the next 3 problems do you think you will solve correctly?
Exit 1
x + 9 = 14
Exit 2
3x - 4 = 11
Exit 3
4x + 2 = 2x + 12
Knowing what you understand is part of learning what to try next.