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3x+15+5x=-1

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3 Answers

Hi Danielle,

Let's talk about the steps to solve single variable equations. (3x + 15 + 5x = -1)

1.  Combine LIKE terms on the same side of the equal sign

That means add apples to apples and oranges to oranges.  In the equation given above equation there are 4 terms: 3x, 15, 5x and -1.

On the left side of the equal sign 3x and 5x are alike...so we add them. 3x + 5x = 8x

8x + 15 = -1

2. Get all the X terms on one side of the equal sign!

In this problem all of the X terms are on the left side of the equal sign, however in another problem you might have X terms on both the left and the right side.  You can move them to either side, but in general the best side to move them to is the side which keeps the coefficient on the X term positive.  Currently the coefficient on the X term is 8 and positive.  Moving it to the right side would make it negative.

Use INVERSE OPERATIONS of addition and subtracton (listed below in next step) to achieve this.

3.  ISOLATE the X term.

Now that there is only 1 X term in your equation, we need to move everything else away from it...e.g.  now that we have gathered all of our apples, we need to move the oranges, bananas and strawberries away from it so that the apples are ISOLATED...or by themselves.

USE INVERSE OPERATIONS to accomplish this...

INVERSE OPERATION

  • If the operation was addition, use subtraction
  • If the operation was subtraction, use addition
  • If the operation was multiplication, use division
  • If the operation was division, use multiplication

8x + 15 - 15 = (-1) - 15

8x + (15 - 15) = (-1) + (-15) <-- you can always change subtraction to addition like this

8x = -16

The X is now isolated...it is on the left side of the the equal sign...all by it's lonesome.

4. Make the coefficient on the X term 1 (MUST BE POSITIVE).

Currently the coefficient on the X term is 8, but since we want it to be 1, we should divide 8x by its current coefficient because 8÷8 =1. REMEMBER, whatever we do to one side we must do to the other!

(8x) ÷ 8 = -16 ÷ 8

 x = -2

5. ALWAYS, ALWAYS CHECK YOUR ANSWER...

Algebra is the only class where a math teacher can not go easy on you while grading and my favorite math teacher showed me that the difference between an A and a B is this step...because you can prove that your answer is CORRECT!

Check your answer by replace X with the derived value of 2 in the ORIGINAL equation.  I know it may seem easier to plug it into 8x + 15 = -1 or 8x = -16, but these are INTERMEDIATE STEPS and if you made a mistake between the ORIGINAL equation and these steps you won't have proven that your answer is correct. So instead we use:

3x + 15 + 5x = -1

3(-2) + 15 + 5(-2) = -1

To complete this problem we will need to use Order of Operation (PEMDAS)...just remember use PEMDAS left to right ALWAYS and you'll never go wrong.

-6 + 15 + (-10) = -1

(-6 +15) + (-10) = -1

9 + (-10) = -1

-1 = -1 <-- We have proven that x= -2 is the solution to this problem.

The steps I have outlined above can be used for any single variable equation no matter how many terms exist in the original equation.  I like to use parentheses () around negative numbers so that I don't lose them...it helps me cut down on the amount of rework when my check tells me that my answer is incorrect.

Danielle,

It is simple: Keep all the unknowns (x 's) on the Left Hand Side (LHS) and move all the known to the Right Hand Side (RHS), so we have:

8x = -16

or x = -2.

now check your answer, by substituting the value of x in the first equation:

3x +15+5x = -1

So, LHS becomes (with x =-2): 3*-2+15+5*-2 = -1 which is what RHS is, so the answer is correct.

This is the way to check all your algebra equations that you solve for an unknown (x).

Hope you have a better understanding!

Gopi M.

It's not as hard as you think it is. The first step is to combine like terms....what are those? Like terms are constants and variables that share qualities. For example you have two terms her with the variable "x". to combine them, look at the sign that is in front of them and add them together. The coefficient "3" here is positive since there is no negative sign. So you will add 3x and 5x. Next you must maneuver things to get the variable to stand alone on one side of the equals sign. The trick really is to make sure that the statement remains true. For example, let's say you have 2+5x=13. If you just move the 2 to the other side of the equation you would have 5x=12-2 (or 15). Would that statement be true if x=1? No, because 5 x 1 = 5 and 5 does not equal 10. So whatever you do to one side you must always do to the other side to keep the equation blanced. Thenxt thing to remember isthat if you want to eliminate a term from one side you must use the opposite function, then use that same function on the otherside. In the case of 2 + 5x = 12 you would subtract 2 from both sides because the two is positive and is added to the other term. Our equation now reads 5x = 10 The opposite function of multiplication is devision so we divide both sides by 5. Now our x is standing alone. And 10 divided by 5 equals 2, so we now know that x=2 You always want to go back and check your work to be sure you came up wit the right answer. to do this, just plug your value into the original equation. I used 2 + 5x = 12 in this example. So you would write 2 + 5 * 2 = 12. Follow the order of operations (PEMDAS) and complete the multiplication first. 5 * 2 = 10. Then complete the addition, 2 + 10 = 12. Our equation is equal! In your case, the second step will involve subtracting a number from a negative number. Since you are really just adding values to the left of the zero you add their absolute value and keep the negative symbol. The final step will involve dividing a negative number by a positive, in which you follow the rule Neg/Pos=Neg. If this helped, make sure to click the thumbs up button. If you are still confused let me know which step and I'll do my best to clear it up for you!