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Word problems involve students finding mathematical answers from textual facts of a particular problem. When we run across a word problem, it's important to make sure to read it and even reread it to make sure we truly understand what the problem is asking for. Does it want us to add, subtract, multiply, or divide? Or does it want us to perform more than one operation? If we can state the problem in our own words, it's more likely that we will be able to grasp what exactly it's asking for, and therefore figure out how to answer it correctly.

Once we know what the problem is asking for, we create a mathematical plan on how to solve it, put the plan into action, and solve the problem, but we're not done yet. We must check back with the original problem and make sure that our solution makes sense. If the problem is asking for the price of three boxes of crackers and somehow we have come up with $\$120$ , we probably want to review our calculations.

Before we start solving equations, we'll discuss how we can write a two-step equation from a verbal model. We use certain keywords to designate particular mathematical operations, such as the following:

- Addition: sum, plus, and, altogether, combined, more than, greater than, longer than, older than, taller than, heavier than, increased
- Subtraction: difference, subtract, left, decreased, shorter than, younger than, lighter than, diminished by
- Multiplication: product, times
- Division: quotient, divided, split up

**Example 1**

Five less than two times a number is equal to ten.

First, identify the keywords that indicate the operations to use.

The phrase "less than" indicates subtraction and "two times" indicates multiplication by 2, such as $2x$ .

So the equation is $2x-5=10$ .

$2x-5+5=10+5$

$2x=15$

$x=7.5$

**Example 2**

Kelley paid $\$145$ for jewelry and shoes. She paid $\$63$ more for shoes than she did for jewelry. How much did Kelley pay for the jewelry?

So, the amount paid for shoes is $\$63$ more than the amount paid for jewelry.

The phrase "more than" indicates an addition operation.

The way to express what she paid for shoes is $x+63$ .

The total amount paid is the sum of the amount paid for both jewelry and shoes.

We can write an equation that represents the situation like this:

$145=x+\left(x+63\right)$

The first step is to combine like items.

$145=2x+63$

Then subtract 63 from both sides.

$82=2x$

Finally, divide each side by 2.

$41=x$

This lets you know that Kelley paid $\$41$ for jewelry. It also lets you know that Kelley paid $\$104$ for the shoes. You can check that answer by adding $\$41$ and $\$104$ , which equals $\$145$ , which is the correct total.

Solving Two-Step Linear Inequalities

College Algebra Diagnostic Tests

Solving word problems with two-step linear equations can be difficult for some students. If your student needs help with these types of problems, pair them with a tutor who can meet them in a 1-on-1 setting and walk them through the process. To learn more about how tutoring can help your student understand word problems with two-step linear equations, contact the Educational Directors at Varsity Tutors today.

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