Certainly! Solving one-step and two-step equations is a fundamental skill in algebra. Here’s a brief overview and some examples to help clarify how to apply this knowledge.
One-Step Equations
A one-step equation can be solved in just one operation (addition, subtraction, multiplication, or division).
Example 1: Addition \[ x + 7 = 12 \] To solve for \(x\), subtract 7 from both sides: \[ x = 12 - 7 \] \[ x = 5 \]
Example 2: Subtraction \[ y - 4 = 10 \] To solve for \(y\), add 4 to both sides: \[ y = 10 + 4 \] \[ y = 14 \]
Two-Step Equations
Two-step equations require two operations to solve.
Example 1: \[ 2x + 3 = 11 \] First, subtract 3 from both sides: \[ 2x = 11 - 3 \] \[ 2x = 8 \] Then, divide by 2: \[ x = \frac{8}{2} \] \[ x = 4 \]
Example 2: \[ 3y - 5 = 10 \] First, add 5 to both sides: \[ 3y = 10 + 5 \] \[ 3y = 15 \] Then, divide by 3: \[ y = \frac{15}{3} \] \[ y = 5 \]
Application
To apply one-step and two-step equations, you can follow these general steps:
- Identify the operation needed to isolate the variable.
- Perform the inverse operation to both sides of the equation.
- Simplify if necessary, and solve for the variable.
- Check your work by substituting the solution back into the original equation to see if both sides are equal.
Practice Problems
Try solving the following one-step and two-step equations:
- \(x + 9 = 20\) (One-step)
- \(5y = 25\) (One-step)
- \(4x - 7 = 21\) (Two-step)
- \(6 + 2z = 18\) (Two-step)
Feel free to ask for more examples or specific applications!
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