2.5(4k+2)=12k
So on this expression for example, how do i figure out on what side i need to move everything to that will give me the correct answer. You move the k to the left side and it comes to -2.5 which is incorrect, but if you move it to the right side then it comes to 2.5 which is the correct answer. Please help it make sense to me. Ive never been good at algebra and im trying to use khan to get me a headstart before i start college again, thank you
It doesn't matter which side of the equals sign you move things around as long as you're careful with your signs. Both sides should give you the same answer. I'll solve it in both ways below.
Solving for "k" (moving "k" to the left side of the equals sign):
[original equation] 1.5(4k+2) = 12k
[multiply the 1.5 into the parenthesis] 6k+3 = 12k
[subtract 12k from both sides] 6k+3-12k = 12k-12k ; [you get] 3 - 6k = 0
[subtract 3 from both sides] 3 - 6k - 3 = 0 - 3 ; [you get] -6k = -3
[divide both sides by -6] -6k/-6 = -3/-6 ; [you get] k = 1/2
Solving for "k" (moving "k" to the right side of the equals sign):
[original equation] 1.5(4k+2) = 12k
[multiply the 1.5 into the parenthesis] 6k+3 = 12k
[subtract 6k from both sides] 6k+3-6k = 12k-6k ; [you get] 3 = 6k
[divide both sides by 6] 3/6 = 6k/6 ; [you get] k = 1/2
So in both cases, as you can see above, you get "k=1/2". Just go slow and make sure your signs are right as you move things around. But there is nothing tricky about it here, both sides of the equal sign works.
Hope this helps!
One thing that might make this easier is that you actually don’t need to decide which side the variable has to go to. You can move the terms either way, as long as you perform the same operation on both sides of the equation.
Also, I noticed the original question says 2.5(4k+2) = 12k, but the example above uses 1.5, so the answers would be different.
For the general idea, think of the equals sign like a balance scale. If you subtract 12k from the left side, you also have to subtract 12k from the right side. You might get a negative coefficient, such as -6k = -3, but that’s completely okay! When you divide both sides by -6, the negatives cancel and you still get a positive answer.
So rather than thinking “I have to move k to the correct side,” try thinking:
“Which operation will make the equation simpler?”
You can put the variable on either side. The important thing is that you do the same thing to both sides.
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