Here’s a real number line like one we saw in the last lesson. Some of the points are labeled with numbers.

Click the "Submit" button after entering your answer.

Now, let’s move on with today’s lesson.

At the beginning of the school year, Aleisha and Danny shared the job of signing up new members for the math club.

Aleisha signed up 6 new members for the club, but she didn’t know how many new members were signed up by Danny.

The number of new members signed up by Aleisha is a known value that can be represented by an actual number.

The number of students signed up by Danny is an unknown value. It can’t be represented by an actual number. Instead, we represent it by a symbol, such as the letter x, which known as a variable.

Which of the following represents the total number of new members? Click the "Submit" button after selecting your answer.

Even though we don’t know the number of new members signed up by Danny, we are able to represent the total number of new club members with an algebraic expression: x + 6.

An algebraic expression consists of one or more numbers and variables, that are related by one or more mathematical operators. Now, let’s see how we can make use of our expression.

During the first meeting of the math club, Aleisha discovers that there are 10 new club members.

Now, we can make a verbal expression about the total new club members: “x plus 6 is equal to 10.”

A mathematical statement such as this, that contains one or more variables is known as an open sentence.

If an open sentence contains an ‘equals’ sign it is called an equation.

Which of the following equations matches our verbal expression regarding the new math club members? Click the "Submit" button after selecting your answer.

We now have an equation: x + 6 = 10.

If we substitute the variable x in our equation with the number 4, our equation is true.

A value for a variable that makes an open statement true is known as a solution.

The solution to our equation tells us that Danny signed up 4 new members for the math club.

Now, let’s practice translating word expressions into algebraic expressions.

Type an algebraic expression that matches the given word expression into the equation area.

After entering the expression in the equation box, click the “Answer” button to display the correct answer and compare it to your own. Then click the “Next” button to go on to the next example.

Now, let’s practice creating an equation to solve a problem. Maria is 6 years old.

She is 5 years younger than her brother Lorenzo. We want to find out Lorenzo’s age.

Let’s have the variable L represent Lorenzo’s age.

Which of the following is an expression for Maria’s age in terms of Lorenzo’s age? Click the "Submit" button after selecting your answer.

Now, we have an expression for Maria’s age: L - 5. We also know that Maria’s age is 6 years old.

We can use this information to create an equation that contains Lorenzo’s age as a variable.

Which of the following is a correct equation based on the known information? Click the "Submit" button after selecting your answer.

We now have an equation containing the variable for Lorenzo’s age: L - 5 = 6.

We see that the equation is true if L is equal to 11.

The solution to our equation is Lorenzo’s age. He is 11 years old.

In this example, we guessed a solution to our equation. In future lessons, we will learn several methods for finding the solutions of equations.

Copyright 2006 The Regents of the University of California and Monterey Institute for Technology and Education