step by step solve equation
0.1(w+0.5) +0.2w =0.2 (w-0.4)
0.1 (w + 0.5) + 0.2w = 0.2(w - 0.4);
0.1w + 0.05 + 0.2w = 0.2w - 0.08;
0.1w + 0.05 = -0.08;
0.1w = -0.13;
w = -1.3
Just wanted to point something extra out. This really is just my own personal preference but its something to look out for that I think can make this problem a bit easier. Multiply every term by 10, which is to say the move the decimal places once to the right.
(10)0.1(w+0.5) +(10)0.2w =(10)0.2 (w-0.4)
w + 0.5 + 2w = 2(w-0.4)
Now, you're only dealing with one decimal place instead of two (0.05), the 0.1w and 0.2w are gone. It works because every term has a number whose sole digit has a place value of one tenth. The answer won't change but I feel that its easier to work with as many integers as possible.
So, without giving you the answer completely, I'll give you some step by step hints. You want to solve for w, so the way to do that is to get w all on it's own on one side of the equation. Start by simplifying the equation - multiply the 0.1 by (w+0.5) and then on the other side of the equation, multiply the 0.2 by the (w-0.4). Once you do that, you'll see you have a bunch of terms that contain w, and a bunch of terms that are just numbers. Work on combining like terms, and then put the w term on one side of the equation, the number term on the other using appropriate addition or subtraction. Then you'll just have to divide both sides by the coefficient in front of the w to get w on its own, and that will be your answer. Hope this helps get you started!
First, we check to see if there is anything that can be done within the parenthesis (remember PEMDAS). Since there isn't, we move to distributing everything on both sides of the equation.
- 0.1(w + 0.5) + 0.2w = 0.2(w - 0.4)
- 0.1(w) + 0.1(0.5) + 0.2w = 0.2(w) + 0.2(-0.4)
- 0.1w + 0.05 + 0.2w = 0.2w - 0.08
Next, we combine like terms on both sides of the equation. Then we isolate the variables on one side and the numerical values on the other, adding/subtracting as necessary.
- (rewrite) 0.1w + 0.2w +0.05 = 0.2w - 0.08
- 0.3w + 0.05 = 0.2w - 0.08
- 0.3w - 0.2w + 0.05 - 0.05 = 0.2w - 0.2w - 0.08 - 0.05
- 0.1w = -0.13
Finally, we divide out the coefficient on the variable on both sides of the equation, and we're done.
- 0.1w/0.1 = -0.13/0.1
- w = -1.3
If you like, let's double check by substituting our answer into the original equation and see if the sides match.
- 0.1(-1.3 + 0.5) + 0.2(-1.3) = 0.2(-1.3 - 0.4)
- 0.1(-0.8) + 0.2(-1.3) = 0.2(-1.7)
- -0.08 - 0.26 = -0.34
- -0.34 = -0.34 :)