Solving One-Variable Equations
Grade 7th Grade · Math · 45 min
What's Included
Learning Objective
I can solve one-variable equations using inverse operations.
Reading Passage
Solving Equations with Inverse Operations
Imagine an equation as a balanced scale. To keep the scale balanced, whatever you do to one side, you must do to the other. Solving equations means finding the value of the variable that makes the equation true. We do this by isolating the variable on one side of the equation using inverse operations.
Inverse operations are operations that undo each other. Addition and subtraction are inverse operations, and so are multiplication and division. For example, to solve the equation x + 5 = 12, we need to isolate x. Since 5 is being added to x, we subtract 5 from both sides of the equation: x + 5 - 5 = 12 - 5. This simplifies to x = 7. So, the solution to the equation is x = 7.
Let's look at another example. To solve the equation 3x = 18, we need to isolate x. Since x is being multiplied by 3, we divide both sides of the equation by 3: 3x / 3 = 18 / 3. This simplifies to x = 6. Therefore, the solution to the equation is x = 6.
Sometimes, you might need to use more than one inverse operation to solve an equation. For example, to solve 2x + 3 = 9, first subtract 3 from both sides: 2x + 3 - 3 = 9 - 3, which simplifies to 2x = 6. Then, divide both sides by 2: 2x / 2 = 6 / 2, which simplifies to x = 3. So, the solution is x = 3.
Remember to always perform the same operation on both sides of the equation to keep it balanced and find the correct value for the variable.
Guided Notes
3 key concepts
- 1
When solving equations, it's helpful to imagine a balanced scale, where you must do the same operation to both sides to keep it balanced.
- 2
Inverse operations are operations that undo each other, such as addition and subtraction, or multiplication and division.
- 3
To solve the equation 2x + 3 = 9, you would first subtract 3 from both sides, then divide both sides by 2, resulting in x = 3.
Practice Questions
7 questions · Multiple choice & Short answer
Exit Ticket
Quick comprehension check
“Solve for x: 4x - 7 = 13. Show all steps.”
Complete Lesson Package
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