Question

Unit 7 Sample Work One and Two Step Equations: Apply

Answer 1

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:

1. **Identify the operation** needed to isolate the variable.
2. **Perform the inverse operation** to both sides of the equation.
3. **Simplify** if necessary, and solve for the variable.
4. **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:

1. \(x + 9 = 20\) (One-step)
2. \(5y = 25\) (One-step)
3. \(4x - 7 = 21\) (Two-step)
4. \(6 + 2z = 18\) (Two-step)

Feel free to ask for more examples or specific applications!