Solving problems with two-step equations typically involves translating a word problem into a mathematical equation and then solving for the variable. Here’s a general approach, along with some examples:
Steps to Solve Two-Step Equations:
-
Understand the problem: Read the problem carefully to identify what is being asked and what information is given.
-
Translate into an equation: Define a variable to represent the unknown quantity. Write an equation based on the relationships and operations described in the problem.
-
Solve the equation:
- Step 1: Isolate the term with the variable by adding or subtracting.
- Step 2: Solve for the variable by multiplying or dividing.
-
Check your solution: Substitute your solution back into the original equation or context to ensure it makes sense.
Examples:
Example 1:
A number is multiplied by 3, and then 4 is added to the result, making 19. What is the number?
Step 1: Define the variable.
Let \( x \) represent the number.
Step 2: Write the equation.
The equation based on the problem is:
\[ 3x + 4 = 19 \]
Step 3: Solve the equation.
-
First, subtract 4 from both sides:
\[ 3x + 4 - 4 = 19 - 4 \]
\[ 3x = 15 \] -
Next, divide by 3:
\[ x = \frac{15}{3} \]
\[ x = 5 \]
Step 4: Check the solution.
Substituting back:
\[ 3(5) + 4 = 15 + 4 = 19 \]
This is correct.
Example 2:
A number decreased by 7 equals 12. What is the number?
Step 1: Define the variable.
Let \( y \) represent the number.
Step 2: Write the equation.
The equation is:
\[ y - 7 = 12 \]
Step 3: Solve the equation.
- Add 7 to both sides:
\[ y - 7 + 7 = 12 + 7 \]
\[ y = 19 \]
Step 4: Check the solution.
Substituting back:
\[ 19 - 7 = 12 \]
This is correct.
Summary:
By identifying the variable, writing the correct equation, and following the steps to solve it, you can effectively tackle a variety of problems involving two-step equations. Practice with different types of problems to improve your skills!