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## Pre-algebra

### Course: Pre-algebra > Unit 7

Lesson 1: Algebraic equations basics# Intro to equations

CCSS.Math:

Learn what an equation is and what it means to find the solution of an equation.

## What is an equation?

**An equation is a statement that two expressions are equal.**For example, the expression 5, plus, 3 is equal to the expression 6, plus, 2 (because they both equal 8), so we can write the following equation:

All equations have an equal sign (equals). The equals sign is

*not*an operator like addition (plus) or subtraction (minus) symbols. The equal sign doesn't tell us what to*do*. It only tells us that two expressions*are*equal. For example, in:The minus sign tells us what to do with 6 and 2: subtract 2 from 6. However, the equals sign does

*not*tell us what to*do*with 6, minus, 2 and 3, plus, 1. It only tells us that they*are equal*.Let's make sure we know the difference between an expression and an equation.

## True equations

All of the equations we just looked at were

**true equations**because the expression on the left-hand side was equal to the expression on the right-hand side. A**false equation**has an equals, but the two expressions are*not*equal to each other. For example, the following is a false equation.When we see an equation that's not true, we can use the not equal sign (does not equal) to show that the two expressions are not equal:

Let's make sure we understand what a true equation is.

## Solutions to algebraic equations

All of the equations that we've looked at so far have included only numbers, but most equations include a variable. For example, the equation x, plus, 2, equals, 6 has a variable in it. Whenever we have an equation like this with a variable, we call it an

**algebraic equation**.For an algebraic equation, our goal is usually to figure out what value of the variable will make a true equation.

For the equation x, plus, 2, equals, 6, notice how start color #7854ab, x, equals, 4, end color #7854ab creates a true equation and start color #ca337c, x, equals, 3, end color #ca337c creates a false equation.

True equation | False equation |
---|---|

$\begin{aligned} \purpleD x +2 &= 6 \\\\\purpleD{4} +2 &\stackrel{?}{=} 6\\\\6 &= 6 \end{aligned}$ | $\begin{aligned} \maroonD x +2 &= 6\\\\\maroonD{3} +2 &\stackrel{?}{=} 6\\\\5 &\neq 6 \end{aligned}$ |

*Notice how we use the symbol equals, start superscript, question mark, end superscript when we're not sure if we have a true equation or a false equation.*

The value of the variable that makes a true equation is called a

**solution to the equation.**Going back to our example, x, equals, start color #7854ab, 4, end color #7854ab is a solution of x, plus, 2, equals, 6 because it makes the equation true.## Let's try a few problems

## Want to join the conversation?

- what is a true equation and a false equation?(38 votes)
- I think it is what makes the equation true like for example - 6+B= 7 true equation would be 1 false because six plus one is seven, false equation would be 2 because six plus two would not equal seven it would equal eight.(27 votes)

- is it a equation if its a fraction(22 votes)
- It can be, if it shows something like 1/2=2/4 (with an equal sign), but it is only an expression if it has no equal sign. For example, 3/8(3 votes)

- What do we do when its a decimal??(28 votes)
- The same thing you do with whole numbers(9 votes)

- What is a true equation and a false??(13 votes)
- True is when the equation is correct. For example, if I were to write the equation 9+9 = 10+8, it would be true because both sides equal 18. However, if I were to write the equation 9+9 = 9+8, it would be false because one side equals 18 and one side equals 17.(22 votes)

- So it can still be an equation even if it has flopped Around?(12 votes)
- Yes;
`2x + 3 = 4`

=`4 = 3 + 2x`

, and I think you mean "flipped." :)(17 votes)

- what does the 3rd question in problem 3 mean(16 votes)
- It means 10=2w =?

Well, using common knowledge we know that 2 x ? = 10

If a variable is next to a number, has a floating period or has parenthesis we must multiply it.

HOPE IT HELPS!!(12 votes)

- how come we mostly use x? shouldn't it be something that makes sense like if its 5x6 shouldn't it be something like 5xS because the first letter of 6 is s?? not sure but just a thought.(11 votes)
- I am pretty sure it is because X is a relatively uncommon letter in the alphabet, for example if we used "a" more regularly it could get confusing.(8 votes)

- What is the difference between a true equation and a false equation?(7 votes)
- a true equation would have both sides the same. for a false equation both sides are not the same.there you go!(13 votes)

- An HMO pamphlet contains the following recommended weight for women: " give yourself 100 pounds for the first 5 feet plus 5 pounds for every inch over 5 feet tall." Using this description , what height corresponds to an ideal weight of 135 pounds? Use X and Y(8 votes)
- We can break 135 pounds into 100+35. The woman must be more than 5 ft tall, and we are looking for how many inches more than 5 feet is the woman. We know for every inch, the ideal weight increases 5 pounds; therefore, for 35 pounds, the woman must be 7 inches taller than 5 feet. Y=5X, where Y is the weight and x is the height in inches surplus 5 feet.(4 votes)

- How do you know what g equals if i doesnt say i am so confused :(5 votes)
- It depends on the problem. But let me give an example!

4=2.2g

We would first have to subtract 2.2 from 4 to get 1.8.

Next we have it plug in 1.8 as g.

Finally check it to see if it makes sense!

Hope that helped!(4 votes)