As long as you do the same operation on both sides of the equality sign and your equation is true for some value of x, the resulting equation will be true. We want to choose a sequence of operations so that eventually our equation will look like x = blah where blah is a purely numerical expression with no unknowns.
The sequence that is usually most convenient is to use PEMDAS backwards. Ie., first you do addition/subtraction until that doesn't help anymore, then you do multiplication/division until that doesn't help any more, then you take care of exponents until that does help, then you remove parentheses and start over from addition/subtraction. This process continues until you have isolated x so that x = blah.
In this case, we have 2x + 30 = 180. First we look for additions/subtractions. we notice that we can get rid of the 30 on the wrong side by subtracting 30 from both sides. We get 2x + 30 - 30 = 180 - 30, or 2x = 150. There are no more additions/subtractions, so we move on.
We notice that we can divide both sides by 2 to get x alone on the left hand side of the equation. We get 2x/2 = 150/2, or x = 75. x has been isolated, so we are done.
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Verified answer
2x = 150
x = 75
As long as you do the same operation on both sides of the equality sign and your equation is true for some value of x, the resulting equation will be true. We want to choose a sequence of operations so that eventually our equation will look like x = blah where blah is a purely numerical expression with no unknowns.
The sequence that is usually most convenient is to use PEMDAS backwards. Ie., first you do addition/subtraction until that doesn't help anymore, then you do multiplication/division until that doesn't help any more, then you take care of exponents until that does help, then you remove parentheses and start over from addition/subtraction. This process continues until you have isolated x so that x = blah.
In this case, we have 2x + 30 = 180. First we look for additions/subtractions. we notice that we can get rid of the 30 on the wrong side by subtracting 30 from both sides. We get 2x + 30 - 30 = 180 - 30, or 2x = 150. There are no more additions/subtractions, so we move on.
We notice that we can divide both sides by 2 to get x alone on the left hand side of the equation. We get 2x/2 = 150/2, or x = 75. x has been isolated, so we are done.
in the long hand
2x+30=180
-30 -30
2x=150
/2 /2
x=75
2x+30=180
-30 -30
=========
2x+0=150
--------
2x=150
/2 /2
======
x=75
2x + 30 = 180
2x = 150
x = 75
First, subtract 30 from each side of the equal sign.
2x = 150
Then divide each side by 2.
x = 75
75
75
First you subtract 30 from both sides and you get 2x = 150.
Then you divide both sides by two and you get x = 75.
2x=180-30
2x=150
x=150/2
x=75