Grade 10 Algebra: Balance in Equations
This worksheet focuses on understanding and applying the concept of balance in algebraic equations for Grade 10 students.
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Grade 10 Algebra: Balance in Equations
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Read each question carefully and answer to the best of your ability. Show all your work for short answer and problem-solving questions. Remember the principle of balance in equations: whatever you do to one side, you must do to the other.
1. What operation would you perform to isolate 'x' in the equation x + 7 = 15?
Add 7 to both sides
Subtract 7 from both sides
Multiply both sides by 7
Divide both sides by 7
2. If an equation is balanced, and you multiply one side by 3, what must you do to the other side to maintain balance?
Add 3
Subtract 3
Multiply by 3
Divide by 3
3. To solve for a variable in an equation, we must perform inverse operations to keep the equation .
4. If you have the equation 3x = 21, you would both sides by 3 to find the value of x.
5. Adding the same number to both sides of an equation maintains its balance.
True
False
6. Dividing one side of an equation by a number and adding that same number to the other side will maintain balance.
True
False
7. Consider the balanced scale above. If the left side represents 'x + 5' and the right side represents '12', what is the value of 'x'?
8. Explain why performing the same operation on both sides of an equation is crucial for finding the correct solution.
9. A carpenter is building a rectangular table. The perimeter of the tabletop is 20 feet. If the length of the table is 6 feet, write and solve an equation to find the width of the table. Show all your steps, demonstrating how you maintain the balance of the equation.
10. Imagine the triple beam balance above represents an algebraic equation. If you add 5 grams to the left pan, what must you do to the right pan to keep the balance level? Relate this to solving equations.