Solve 2 Step Equations with Ease - Free Word Problems

Understanding 2-Step Equations

Math can be a challenge for many students, but with the right approach, solving equations can become a breeze. Two-step equations are a fundamental concept in algebra, and mastering them is essential for success in math. In this article, we’ll explore what two-step equations are, how to solve them, and provide some examples with word problems.

What are 2-Step Equations?

A two-step equation is a linear equation that requires two operations to solve for the variable. These operations can be addition, subtraction, multiplication, or division. Two-step equations are typically represented in the form of ax + b = c, where a, b, and c are constants, and x is the variable.

How to Solve 2-Step Equations

Solving two-step equations involves two main steps: isolating the variable and performing the necessary operations. Here’s a step-by-step guide to solving two-step equations:

1. Read the equation carefully: Understand the equation and identify the variable, constants, and operations involved.
2. Perform the first operation: Perform the first operation to isolate the variable. This can be addition, subtraction, multiplication, or division.
3. Perform the second operation: Once you’ve isolated the variable, perform the second operation to solve for the variable.

📝 Note: When solving two-step equations, it's essential to follow the order of operations (PEMDAS): Parentheses, Exponents, Multiplication and Division, and Addition and Subtraction.

Examples of 2-Step Equations

Let’s solve some examples of two-step equations:

Example 1: 2x + 5 = 11

• Step 1: Subtract 5 from both sides (2x = 11 - 5)
• Step 2: Divide both sides by 2 (x = ⁶⁄₂)
• Solution: x = 3

Example 2: x - 3 = 7

• Step 1: Add 3 to both sides (x = 7 + 3)
• Step 2: Simplify the equation (x = 10)
• Solution: x = 10

Word Problems with 2-Step Equations

Word problems can be a great way to apply two-step equations to real-life scenarios. Here are some examples:

Example 1: Tom has been saving money for a new bike and has 120 in his savings account. He wants to buy a bike that costs 180. If he earns $15 per hour, how many hours will he need to work to have enough money to buy the bike?

• Let x be the number of hours Tom needs to work.
• Equation: 15x + 120 = 180
• Step 1: Subtract 120 from both sides (15x = 60)
• Step 2: Divide both sides by 15 (x = ⁶⁰⁄₁₅)
• Solution: x = 4 hours

Example 2: A bakery sells a total of 250 loaves of bread per day. They sell a combination of whole wheat and white bread. If they sell 30 more whole wheat loaves than white bread loaves, and they sell 120 whole wheat loaves, how many white bread loaves do they sell?

• Let x be the number of white bread loaves.
• Equation: x + 30 = 120
• Step 1: Subtract 30 from both sides (x = 90)
• Step 2: Simplify the equation (x = 90)
• Solution: x = 90 loaves

More Word Problems

Here are some more word problems to practice solving two-step equations:

• A bookshelf has 5 shelves, and each shelf can hold 8 books. If the bookshelf is currently empty, how many books can be placed on it in total?
• A car rental company charges a base fee of 20 plus an additional 0.25 per mile driven. If a customer rents a car for a day and drives 120 miles, how much will they be charged in total?
• A group of friends want to share some candy equally. If they have 48 pieces of candy and there are 8 friends, how many pieces of candy will each friend get?

Conclusion

Solving two-step equations can seem intimidating at first, but with practice and patience, it becomes easier. By following the steps outlined in this article and practicing with word problems, you’ll become more confident in your ability to solve two-step equations. Remember to always read the equation carefully, perform the necessary operations, and check your work to ensure accuracy.

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