Search 74,092 tutors

# What is x in 7x-2=5x+8

What is x in 7x-2=5x+8

There are 2 types of ways of expressing #s

Type 1:  Think about 7x and 5x as one type of way of expressing two different numbers that you don't know yet.

Type 2:  Think about -2 and 8 as another type of way of expressing a number, and in fact they are numbers.

Rule: You cannot add or subtract Type 1 to Type 2. Only Type 1 can add/subtract to another Type 1. Only Type 2 can add/subtract to another Type 2.

7x - 2 = 5x + 8  Problem

7x - 5x -2 = 8   Subtract 5x from both sides to get rid of

5x on right side

2x -2 = 8          Because 7x and -5x are both Type 1, you

can combine them and get 2x

2x = 10            Add 2 to both sides to get rid of -2 from

left side

x = 10/2 = 5

Isolate x by multiplying (1/2) to both sides to get rid of the coefficient in front of x (which is 2) and that leads you to your answer (5).

Love it - great explanation, Rizul!

1/5/2013

Thanks! I did a lot of editing because of alignment issues so I apologize if you are getting a lot of emails about there being an answer update to this question.

1/5/2013

What is x in 7x-2=5x+8

To solve any equation with variables, you must get like terms on the same side of the equation. To do this you will add or subtract from each side.

7x-2 +2 = 5x + 8 + 2

7x = 5x + 10

7x - 5x = 5x - 5x + 10

2x = 10

Next you would solve for x by dividing.

2x/2 = 10/2

x = 5

What is x in 7x-2=5x+8

To solve an equation you must get the numbers with variables (letters) together on one side of the = and the numbers without variables to the other side of the = using inverse (opposite) operations. Always remember that an equation must stay balanced by doing the same thing to both sides. You can then solve the equation by isolating the variable (getting the letter by itself) on one side of the equation.

So in the equation 7x - 2 = 5x + 8

1) You need to get the 7x and 5x together by subtracting the 5x from both sides. That removes it from the right side and then 7x - 5x = 2x, so the new equation is 2x - 2 = 8.

2) Now you need to add 2 to both sides which removes it from the left side and 8 + 2 = 10, so the new equation is  2x = 10.

3) Now to get x by itself, you would divide both sides by 2, so x is now by itself on the left and 10/2=5. That gives you an answer of x = 5.

4) Check your work by plugging 5 into the original equation for x. 7(5) - 2 = 35 - 2 = 33

AND 5(5) + 8 = 25 + 8 = 33. Since both sides equal the same value when you plug 5 in for x, 5 is the correct value.

Subtract 5x from both sides: 2x - 2 = 8

Next add 2 to both sides: 2x = 10

Finally, divide both sides by 2 to get x = 5

The key to algebra is "BOTH SIDES" (of the  = )!!!!!

An equation (math expression with an equal (=) sign) is like a seesaw or teeter-totter:  both need to remain balanced to work correctly.  If you adjust or change the weight on one side of a seesaw, then you have to also adjust or change weight on the opposite side until it is balanced again.  So in math, whatever you do to one side of an equation you must also do on the other side.

In our example of 7x - 2 = 5x + 8, our goal is to find out how much x needs to "weigh" to balance both sides of the equation.  When you have the correct amount of x and substitute that value for all x's in the equation, both sides will calculate to the same number (our "weight"), and they will be equal or balanced.

How to find x?  Let's get all the x's together, so we can find out.  Let's subtract 5x from the right side, to remove it from there:  5x + 8 - 5x = 8.  But to keep that balance, we also need to subtract the same 5x from the left side:  7x - 5x - 2 = 2x - 2.  So now we can show both sides of our new equation together:

2x - 2 = 8.  To get the 2x by itself, let's add 2, so the left side becomes 2x - 2 + 2 = 2x.  Now to keep balance, we also add 2 to the right side:  8 + 2 = 10.  Putting the two new left and right sides back together:  2x = 10.  On the left side, we can divide 2x by 2 to get x by itself:  2x/2 = x.  On the right side, we need to also divide by 2 to keep balance:  10/2 = 5.  Now we have x = 5, our answer.

Let's check it by substituting 5 for every x in the original equation:

7(5) - 2 = 5(5) + 8;   35 - 2 = 25 + 8;  33 = 33, so now we know for sure that x = 5 is the correct answer!