solve 3x + 2 = 10

Question

solve the following equations

 

1)   3x + 2 = 10

 

2)   2x/3 = 10

 

3)   2(x+4) + 3x = 24

 

4)   -2x + 3 = 35

Answer 1

When solving for x you always work on getting the x all by itself. 

 

What I mean by that is in the first question on the left side of the equation are two things.  One thing is added to the x and the other thing is multiplied by the x (3x means 3 times x).  Undo things that are farther from the x first. 

 

1) 3x + 2 = 10

 

We want to undo + 2 so we subtract 2 from the left side but since we do that we always have to balance things by also doing it to the right side.  Subtraction undoes addition.

 

3x + 2 = 10

     - 2 = - 2

3x = 8

 

Now we need to undo the multiplication by dividing.

 

3x = 8

3   = 3

 

x = 8/3 = 2 2/3 or approximately 2.67

2) 2x/3 = 10

 

Here we want to first deal with the thing (coefficient) that is not in front of the x.  We want to get rid of the 3.  Since the left side is dividing by 3 we undo it by multiplying by 3.

 

2x/3*3 = 10 * 3 (remember that if we do something to one side of the equal side we also have to do it to the left side as well)  

 

We are left now with 2x = 30.  We need to get rid of the 2.  Since 2x means 2 * x we have to divide by 2 to leave the x all by itself.  Again this means dividing both sides of the = sign by 2.

 

2x  =  30

2   =    2

 

x = 30/2 = 15

 

 

3) 2(x+4) + 3x = 24

 

This one is a little trickier.  There are a lot of things going on to the left of the = sign.  You always start by combing the numbers (coefficients) in front of the x.  On this one you do this by first multiplying the 2 in front of the ().

 

2(x+4) means that we are multiplying the 2 by everything in between the ( and the ).  So in this case we have

2 times x and 2 times +4.  This gives us 2x + 8

 

Now we have 2x + 8 + 3x = 24.  Now we can add the numbers in front of the x's together.  2x + 3x = 5x.

 

We now have 5x+8=24 which looks just like the first two we did.  So first we get rid of the 8 using subtraction and then the 5 in front of the x by division.

 

5x + 8 = 24

     - 8 = -8

5x = 16

 

5x = 16

5  = 5

 

x = 16/5 = 3 1/5 or 3.2

4) -2x + 3 = 35

 

This one is very similar to the others we have done before.  The only difference that we see is that the number in front of the x is a negative number.  This simply means that we have -2 times x and when we get to the step where we divide we simply divide both sides by a -2.  Remember that we have a positive 35 on the right side and our answer will be a positive number divided by a negative number which will give us a negative answer.

 

-2x + 3 = 35

      - 3 = - 3    (always take care of the number that doesn't have an x behind it first)

-2x = 32

 

-2x = 32

-2 = -2

 

x = 32/-2 = -16

Answer 2

1). 3x + 2 = 10

First, you need to subtract 2 from each side.

 

3x = 8

Then, you need to divide both sides by 3.

 

x = 2.67 (rounded from 2.66666667)

 

2). 2x / 3 = 10

First you need to multiply both sides by 3, which cancels out the denominator on the left side

 

2x = 30

Then, you need to divide both sides by 2

 

x = 15

 

3). 2 (x+4) +3x = 24

First, you need to distribute. Multiply 2 by x to get 2x, then 2 by 4 to get 8.

 

2x + 8 + 3x = 24

Then, add the 2x and 3x.

 

5x + 8 = 24

Next, subtract 8 from both sides.

 

5x = 16

Finally, divide both sides by 5.

 

x = 3.2

 

4). -2x + 3 = 35

First, subtract 3 from both sides.

 

-2x = 32

Then, divide both sides by -2.

 

x = -16

 

 

I hope this helps you now and with future math homework!