Year 7 Maths: Which x Satisfies an Equation?

Introduction to Equations

Hello, Year 7! Today, we are going to learn about equations and how to find the value of ( x ) that makes them true. An equation is like a balance scale. Both sides must be equal for it to work!

What is an Equation?

An equation is a math statement that shows two expressions are equal. For example, in the equation:

$$

2x + 3 = 11

$$

This means that if we find the right number for ( x ), both sides of the equation will be equal.

Steps to Solve for x

1. Identify the equation: Look for the ( x ) and see what you need to find.
2. Isolate ( x ): You want to get ( x ) all by itself on one side of the equation.
3. Perform the same operation on both sides: Whatever you do to one side, you must do to the other.

Example 1

Let’s solve the equation:

$$

x + 5 = 12

$$

• First, subtract 5 from both sides:

$$

x + 5 – 5 = 12 – 5

$$

• This simplifies to:

$$

x = 7

$$

Now we know that ( x = 7 ) is the answer.

Example 2

Now, let’s try another one:

$$

3x = 15

$$

• To find ( x ), divide both sides by 3:

$$

\frac{3x}{3} = \frac{15}{3}

$$

• This simplifies to:

$$

x = 5

$$

So, ( x = 5 ) is the solution!

Key Rules to Remember

1. Do the same operation on both sides: This keeps the equation balanced.
2. Keep ( x ) on one side: Move other numbers away from ( x ).
3. Check your work: Substitute your ( x ) value back into the original equation to make sure it works.

Tips and Tricks

• Use a pencil: It’s okay to make mistakes; you can erase and try again!
• Write down each step: This helps you stay organised and understand your work better.
• Practice regularly: The more you practice, the easier it gets.

Questions

Easy Level Questions

1. What is ( x ) in the equation ( x + 2 = 5 )?
2. Find ( x ) in ( 4x = 16 ).
3. Solve ( x – 3 = 1 ).
4. What is ( x ) in ( 5 + x = 10 )?
5. Find ( x ) in ( 2x = 8 ).
6. Solve ( x – 4 = 2 ).
7. What is ( x ) in ( 3 + x = 7 )?
8. Find ( x ) in ( x + 6 = 12 ).
9. Solve ( 10 = x + 5 ).
10. What is ( x ) in ( 2x + 3 = 9 )?
11. Find ( x ) in ( x/4 = 3 ).
12. Solve ( x + 1 = 4 ).
13. What is ( x ) in ( 6 = x + 2 )?
14. Find ( x ) in ( x – 5 = 0 ).
15. Solve ( 7 = 2 + x ).
16. What is ( x ) in ( 8 = x + 3 )?
17. Find ( x ) in ( 5x = 25 ).
18. Solve ( 2 + x = 9 ).
19. What is ( x ) in ( x + 8 = 15 )?
20. Find ( x ) in ( x – 2 = 3 ).

Medium Level Questions

1. What is ( x ) in ( 3x + 5 = 20 )?
2. Solve ( 5x – 3 = 2 ).
3. What is ( x ) in ( 2x + 2 = 10 )?
4. Find ( x ) in ( 4x – 4 = 12 ).
5. Solve ( x/3 + 2 = 5 ).
6. What is ( x ) in ( 6x – 1 = 11 )?
7. Find ( x ) in ( x + 2x = 12 ).
8. Solve ( 10 – 2x = 2 ).
9. What is ( x ) in ( 7x + 3 = 24 )?
10. Find ( x ) in ( 2 + 3x = 17 ).
11. Solve ( 4x + 2 = 18 ).
12. What is ( x ) in ( 8 = 2x + 4 )?
13. Find ( x ) in ( 10x + 1 = 31 ).
14. Solve ( 6 = 2x – 2 ).
15. What is ( x ) in ( 7x – 3 = 18 )?
16. Find ( x ) in ( 5 + 4x = 29 ).
17. Solve ( 3x – 6 = 3 ).
18. What is ( x ) in ( 2x/2 = 8 )?
19. Find ( x ) in ( 9x + 1 = 28 ).
20. Solve ( 4 + x = 2x + 1 ).

Hard Level Questions

1. What is ( x ) in ( 5x + 2 = 3x + 10 )?
2. Solve ( 2(x + 3) = 4x – 2 ).
3. What is ( x ) in ( 3(x – 4) = 2x + 3 )?
4. Find ( x ) in ( 4x/2 + 3 = 11 ).
5. Solve ( 2(x – 1) + 3 = 4(x + 1) ).
6. What is ( x ) in ( 5 – 3(x + 1) = 2 )?
7. Find ( x ) in ( 7x + 1 = 3x + 17 ).
8. Solve ( 3(x + 2) = 9 – 2x ).
9. What is ( x ) in ( 4(x + 1) – 2 = 2(x + 5) )?
10. Find ( x ) in ( 2x + 3(2 – x) = 9 ).
11. Solve ( 5x – 2(3 – x) = 3 ).
12. What is ( x ) in ( 10 – 4(x – 1) = 2 )?
13. Find ( x ) in ( 6(x – 2) + 4 = 2(x + 3) ).
14. Solve ( 2(x + 3) = 3 – x ).
15. What is ( x ) in ( 7(x – 1) + 2 = 19 )?
16. Find ( x ) in ( 8 – 2(x + 1) = 0 ).
17. Solve ( 3(x + 1) – 5 = 2x ).
18. What is ( x ) in ( 4(2x – 1) = 3(2x + 5) )?
19. Find ( x ) in ( 5x + 3 = 2(3x + 8) ).
20. Solve ( x/2 + 3(x – 1) = 10 ).

Answers

Easy Level Answers

1. ( x = 3 ) because ( 3 + 2 = 5 ).
2. ( x = 4 ) since ( 4 \times 4 = 16 ).
3. ( x = 4 ) because ( 4 – 3 = 1 ).
4. ( x = 5 ) since ( 5 + 5 = 10 ).
5. ( x = 4 ) as ( 2 \times 4 = 8 ).
6. ( x = 6 ) because ( 6 – 4 = 2 ).
7. ( x = 4 ) since ( 3 + 4 = 7 ).
8. ( x = 6 ) because ( 6 + 6 = 12 ).
9. ( x = 5 ) since ( 10 = 5 + 5 ).
10. ( x = 3 ) because ( 2 \times 3 + 3 = 9 ).
11. ( x = 12 ) because ( 12/4 = 3 ).
12. ( x = 3 ) since ( 3 + 1 = 4 ).
13. ( x = 4 ) because ( 4 = 4 + 2 ).
14. ( x = 2 ) since ( 2 – 2 = 0 ).
15. ( x = 11 ) because ( 7 + 4 = 11 ).
16. ( x = 5 ) since ( 5 + 3 = 8 ).
17. ( x = 5 ) since ( 5 \times 5 = 25 ).
18. ( x = 7 ) because ( 7 + 2 = 9 ).
19. ( x = 7 ) since ( 7 + 8 = 15 ).
20. ( x = 5 ) because ( 5 – 2 = 3 ).

Medium Level Answers

1. ( x = 5 ) because ( 3 \times 5 + 5 = 20 ).
2. ( x = 1 ) as ( 5 \times 1 – 3 = 2 ).
3. ( x = 4 ) since ( 2 \times 4 + 2 = 10 ).
4. ( x = 4 ) because ( 4 \times 4 – 4 = 12 ).
5. ( x = 9 ) since ( 9/3 + 2 = 5 ).
6. ( x = 2 ) because ( 6 \times 2 – 1 = 11 ).
7. ( x = 4 ) since ( 4 + 8 = 12 ).
8. ( x = 4 ) because ( 10 – 8 = 2 ).
9. ( x = 3 ) since ( 7 \times 3 + 3 = 24 ).
10. ( x = 5 ) because ( 2 + 3 \times 5 = 17 ).
11. ( x = 4 ) since ( 4 \times 4 + 2 = 18 ).
12. ( x = 2 ) because ( 8 = 2 \times 2 + 4 ).
13. ( x = 3 ) since ( 10 \times 3 + 1 = 31 ).
14. ( x = 4 ) because ( 6 = 2 \times 4 – 2 ).
15. ( x = 3 ) since ( 7 \times 3 – 3 = 18 ).
16. ( x = 5 ) because ( 5 + 4 \times 5 = 29 ).
17. ( x = 3 ) since ( 3 \times 3 – 6 = 3 ).
18. ( x = 8 ) because ( 2 \times 8/2 = 8 ).
19. ( x = 3 ) since ( 9 \times 3 + 1 = 28 ).
20. ( x = 1 ) since ( 4 + 1 = 2 \times 1 + 1 ).

Hard Level Answers

1. ( x = 4 ) since ( 5 \times 4 + 2 = 3 \times 4 + 10 ).
2. ( x = 5 ) because ( 2(5 + 3) = 4 \times 5 – 2 ).
3. ( x = 9 ) since ( 3(9 – 4) = 2 \times 9 + 3 ).
4. ( x = 8 ) because ( 4 \times 8/2 + 3 = 11 ).
5. ( x = 2 ) since ( 2(2 – 1) + 3 = 4(2 + 1) ).
6. ( x = 2 ) since ( 5 – 3(2 + 1) = 2 ).
7. ( x = 4 ) because ( 7 \times 4 + 1 = 3 \times 4 + 17 ).
8. ( x = 3 ) since ( 3(3 + 2) = 9 – 2 \times 3 ).
9. ( x = 5 ) since ( 4(5 + 1) – 2 = 2(5 + 5) ).
10. ( x = 5 ) because ( 2 + 3(5 – 1) = 9 ).
11. ( x = 3 ) since ( 5 \times 3 + 3(3 – 3) = 3 ).
12. ( x = 5 ) since ( 10 – 4(5 – 1) = 2 ).
13. ( x = 3 ) because ( 6(3 – 2) + 4 = 2(3 + 3) ).
14. ( x = 5 ) since ( 2(5 + 3) = 3 – 5 ).
15. ( x = 3 ) since ( 7(3 – 1) + 2 = 19 ).
16. ( x = 1 ) because ( 8 – 2(1 + 1) = 0 ).
17. ( x = 3 ) since ( 3(3 + 1) – 5 = 2 \times 3 ).
18. ( x = 3 ) since ( 4(2 \times 3 – 1) = 3(2 \times 3 + 5) ).
19. ( x = 7 ) because ( 5 \times 7 + 3 = 2(3 \times 7 + 8) ).
20. ( x = 4 ) since ( x/2 + 3(4 – 1) = 10 ).

Now you have a good understanding of how to find ( x ) in an equation. Keep practicing, and soon it will become second nature!