I am a grade 9 student and I cannot figure out how to solve these two similar problems. can you please help?
-3(y-1/2)=1/2 also -2/3(x + 1)=6
I don't come up with the same answers as the book and I can't figure out what I'm doing wrong.
I want to look at your second problem.
You can think of an equation as a balance with the center at the "=" sign and equal wieghts on either side. The task here is to manipulate the balance, keeping it level, and end with an equation x=... . The operations that keep the balance level are adding or subtraction equal amounts from both sides, or multiplying or dividing both sides by equal amounts.
For your problem -2/3(x + 1)=6 you first need to remove the -2/3 for the left side. This you can do by multipying both sides by -3/2 since (-3/2)(-2/3)=1.
So -2/3(x+1)=6 is equivalent to (-3/2)(-2/3)(x+1)=(-3/2)(6) which is x+1=-9.
If you now subtract 1 from both sides you get x+1-1=-9-1 or x=-10.
To verify that this is the correct answer check to see if the left side of the original equation, -2/3(x + 1), gives a value of 6 when x is -10.
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