Operations and Algebraic Thinking 218-221
Intro to equations
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 is equal to the expression (because they both equal ), so we can write the following equation:
All equations have an equal sign (). The sign is not an operator like addition () or subtraction () symbols. The equal sign doesn't tell us what to do. It only tells us that two expressions are equal. For example, in:
The sign tells us what to do with and : subtract from . However, the sign does not tell us what to do with and . It only tells us that they are equal.
Let's make sure we know the difference between an expression and an equation.
Which of these is an equation?
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 , 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 () to show that the two expressions are not equal:
Let's make sure we understand what a true equation is.
Which of these are true equations?
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 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 , notice how creates a true equation and creates a false equation.
|True equation||False equation|
Notice how we use the symbol 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, is a solution of because it makes the equation true.
Let's try a few problems
Select the solution to the equation.
Want to join the conversation?
- what is a true equation and a false equation?(40 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.(34 votes)
- What do we do when its a decimal??(32 votes)
- The same thing you do with whole numbers(15 votes)
- is it a equation if its a fraction(25 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(6 votes)
- What is a true equation and a false??(14 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.(25 votes)
- So it can still be an equation even if it has flopped Around?(15 votes)
2x + 3 = 4=
4 = 3 + 2x, and I think you mean "flipped." :)(18 votes)
- what does the 3rd question in problem 3 mean(19 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!!(13 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.(14 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.(11 votes)
- What is the difference between a true equation and a false equation?(10 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.(6 votes)
- math is not very bus(9 votes)