Equations

What is an Equation

An equation says that two things are equal. It will have an equals sign "=" like this:

x

+

2

=

6

That equation says: what is on the left (x + 2) is equal to what is on the right (6)

So an equation is like a statement "this equals that"

Parts of an Equation

So people can talk about equations, there are names for different parts (better than saying "that thingy there"!)

Here we have an equation that says 4x − 7 equals 5, and all its parts:

A Variable is a symbol for a number we don't know yet. It is usually a letter like x or y.

A number on its own is called a Constant.

A Coefficient is a number used to multiply a variable (4x means 4 times x, so 4 is a coefficient)

Sometimes a letter stands in for the number:

Example: ax² + bx + c

• x is a variable
• a and b are coefficients
• c is a constant

An Operator is a symbol (such as +, ×, etc) that shows an operation (ie we want to do something with the values).

A Term is either a single number or a variable, or numbers and variables multiplied together.

An Expression is a group of terms (the terms are separated by + or − signs)

So, now we can say things like "that expression has only two terms", or "the second term is a constant", or even "are you sure the coefficient is really 4?"

Writing Algebraic Equations

Problem:	Jeanne has $17 in her piggy bank. How much money does she need to buy a game that costs $68?
Solution:	Let x represent the amount of money Jeanne needs. Then the following equation can represent this problem:
	17 + x = 68
	We can subtract 17 from both sides of the equation to find the value of x.
	68 - 17 = x
Answer:	x = 51, so Jeanne needs $51 to buy the game.

In the problem above, x is a variable. The symbols 17 + x = 68 form an algebraic equation. Let's look at some examples of writing algebraic equations.

Example 1:	Write each sentence as an algebraic equation.
	Sentence Algebraic Equation A number increased by nine is fifteen. y + 9 = 15 Twice a number is eighteen. 2n = 18 Four less than a number is twenty. x - 4 = 20 A number divided by six is eight.

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Example 2:	Write each sentence as an algebraic equation.
	Sentence Algebraic Equation Twice a number, decreased by twenty-nine, is seven. 2t - 29 = 7 Thirty-two is twice a number increased by eight. 32 = 2a + 8 The quotient of fifty and five more than a number is ten. Twelve is sixteen less than four times a number. 12 = 4x - 16

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Example 3:	Write each sentence as an algebraic equation.
	Sentence Algebraic Equation Eleni is x years old. In thirteen years she will be twenty-four years old. x + 13 = 24 Each piece of candy costs 25 cents. The price of h pieces of candy is $2.00. 25h = 200 or .25h = 2.00 Suzanne made a withdrawal of d dollars from her savings account. Her old balance was $350, and her new balance is $280. 350 - d = 280 A large pizza pie with 15 slices is shared among p students so that each student's share is 3 slices.

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Summary:

An algebraic equation is an equation that includes one or more variables. In this lesson, we learned how to write a sentence as an algebraic equation. Resolviendo ecuaciones, para practica