How to do two step equations is an essential algebra skill that helps you find an unknown value by reversing two operations in the correct order. A two-step equation is an equation that requires two inverse operations to isolate the variable, such as 2x + 3 = 11 or x/4 − 5 = 7.
Introduction
In algebra, a variable such as x represents a number whose value is unknown. Because of that, the purpose of solving an equation is to determine that value while keeping both sides of the equation equal. A two-step equation usually combines multiplication or division with addition or subtraction Worth keeping that in mind. Took long enough..
As an example, the expression 3x + 2 means that a number is first multiplied by 3 and then increased by 2. To solve 3x + 2 = 17, you must reverse those operations:
- Subtract 2 from both sides.
- Divide both sides by 3.
The result is x = 5. Checking the answer confirms that 3(5) + 2 = 17, so the solution is correct Small thing, real impact..
What Is a Two-Step Equation?
A two-step equation contains a variable and at least two arithmetic operations. It generally has one of these forms:
- ax + b = c, such as 4x + 1 = 13
- ax − b = c, such as 5x − 8 = 17
- x/a + b = c, such as x/3 + 6 = 10
- x/a − b = c, such as x/2 − 4 = 9
In the first two forms, multiplication is followed by addition or subtraction. In the other forms, division is followed by addition or subtraction. The variable may also appear on either side of the equation, but the same balancing principle applies.
An equation is like a balance scale. On top of that, whatever operation is performed on one side must also be performed on the other side. This keeps the equality true and allows the variable to be isolated safely That's the part that actually makes a difference..
The Five-Step Method for Solving Two-Step Equations
1. Identify the operations
Look at the side of the equation that contains the variable. Determine which operations are being performed on it and in what order.
As an example, in 5x − 4 = 21:
- Multiplication is happening because of 5x.
- Subtraction is happening because 4 is being taken away.
2. Undo addition or subtraction
The first operation to reverse is usually addition or subtraction. Use the inverse operation on both sides of the equation Turns out it matters..
For 5x − 4 = 21, add 4 to both sides:
5x − 4 + 4 = 21 + 4
This simplifies to:
5x = 25
3. Undo multiplication or division
Next, reverse multiplication or division It's one of those things that adds up..
For 5x = 25, divide both sides by 5:
5x ÷ 5 = 25 ÷ 5
This gives:
x = 5
4. Interpret the solution
The value x = 5 is the solution because it makes the original equation true. The equals sign does not mean “the answer comes next”; it means that the expressions on both sides currently have the same value Worth keeping that in mind..
5. Check your answer
Substitute the solution back into the original equation. For 5x − 4 = 21:
5(5) − 4 = 25 − 4 = 21
Because both sides equal 21, the solution is verified.
Worked Example: Addition Followed by Multiplication
Solve:
7x + 3 = 24
First, subtract 3 from both sides:
7x + 3 − 3 = 24 − 3
7x = 21
Then divide both sides by 7:
7x ÷ 7 = 21 ÷ 7
x = 3
Check the result:
7(3) + 3 = 21 + 3 = 24
So, x = 3 That's the part that actually makes a difference..
The order — worth paying attention to. If division is attempted first, the equation becomes unnecessarily complicated. Reversing addition or subtraction first leaves a simple multiplication equation Which is the point..
Worked Example: Division Followed by Subtraction
Solve:
x/6 − 2 = 5
The variable is divided by 6, and 2 is then subtracted. Add 2 to both sides:
x/6 − 2 + 2 = 5 + 2
x/6 = 7
Multiply both sides by 6:
(x/6) × 6 = 7 × 6
x = 42
Check the equation:
42/6 − 2 = 7 − 2 = 5
The answer is correct.
Equations with Negative Coefficients
A coefficient can be negative. In −4x + 7 = −13, the variable is multiplied by −4, and 7 is added.
First, subtract 7 from both sides:
−4x + 7 − 7 = −13 − 7
−4x = −20
Now divide both sides by −4:
(−4x)/(−4) = (−20)/(−4)
x = 5
Check the result:
−4(5) + 7 = −20 + 7 = −13
A negative coefficient does not make
