Two-step algebraic equations involve a bit more complexity than one-step equations, but they follow a similar process. The goal is to isolate the variable by performing two different operations. Here are some examples and explanations to help children understand how to solve two-step equations:
1. Solving Addition and Subtraction
Equation: 2x + 3 = 11
Steps to Solve:
- Understand: You need to find out what number x is when you first multiply it by 2 and then add 3 to get 11.
- Isolate the Variable: Start by subtracting 3 from both sides of the equation to undo the addition. 2x + 3 – 3 = 11 – 3. 2x = 8
- Solve for x: Next, divide both sides by 2 to undo the multiplication.
= 
x = 4 - Check: Substitute 4 back into the original equation to ensure it works. 2 × 4 + 3 = 8 + 3 = 11
This is correct!
Solution: x=4
2. Solving Subtraction and Addition
Equation: x – 5 = 7 + 2
Steps to Solve:
- Understand: You need to find out what number x is when you subtract 5 from it to get the result of 7 plus 2.
- Simplify the Right Side: First, add 7 and 2. X – 5 = 9
- Isolate the Variable: Next, add 5 to both sides to undo the subtraction. X – 5 + 5 = 9 + 5 x = 14
- Check: Substitute 14 back into the original equation to verify. 14 – 5 = 9
This is correct!
Solution: x=14
3. Solving Multiplication and Addition
Equation: 3x + 4 = 19
Steps to Solve:
- Understand: You need to find out what number x is when you multiply it by 3 and then add 4 to get 19.
- Isolate the Variable: Start by subtracting 4 from both sides of the equation. 3x + 4 – 4 = 19 – 4. 3x=15
- Solve for x: Next, divide both sides by 3 to undo the multiplication.
= 
x = 5 - Check: Substitute 5 back into the original equation to ensure it works. 3 × 5 + 4 = 15 + 4 = 19
This is correct.
Solution: x=5
4. Solving Division and Subtraction
Equation: 
– 2 = 3
Steps to Solve:
- Understand: You need to find out what number x is when you first divide it by 4 and then subtract 2 to get 3.
- Isolate the Variable: Start by adding 2 to both sides of the equation. – 2 + 2 = 3 + 2. = 5
- Solve for x: Next, multiply both sides by 4 to undo the division. x 4 = 5 x 4 x = 20
- Check: Substitute 20 back into the original equation to verify.
- 2 = 5 – 2 = 3
This is correct!
Solution: x=20
5. Solving Multiplication and Subtraction
Equation: 4x−7=9
Steps to Solve:
- Understand: You need to find out what number x is when you first multiply it by 4 and then subtract 7 to get 9.
- Isolate the Variable: Start by adding 7 to both sides of the equation.4x – 7 + 7 = 9 + 7 4x=16
- Solve for x: Next, divide both sides by 4 to undo the multiplication.4
= 
x = 4 - Check: Substitute 4 back into the original equation to ensure it works. 4 × 4 – 7 = 16 – 7 = 9
This is correct!
Solution: x=4
Summary
Two-step algebraic equations involve performing two operations to isolate the variable. By following these steps—understanding the problem, isolating the variable, solving, and checking—children can learn to solve more complex equations with ease.