Tutor profile: Anna P.
Find $$(f \circ g) x$$ when $$f(x)=-6x+5$$ and $$g(x)=-9x-11$$.
Remember that $$(f \circ g) x=f(g(x))$$ so we want to substitute $$g(x)$$ in for the $$x$$ in $$f(x)$$ resulting in: $$-6(-9x-11)+5$$. Now all we need to do is simplify by distributing -6 into the parentheses and combining like terms. After distributing we will get: $$54x+66+5$$. We can combine 66 and 5 since they are both constants (terms without a variable). Our final answer would be $$(f \circ g) x=54x+71$$.
Subject: Basic Math
What is the best way to learn multiplication and division of fractions and decimals?
Repetition and practice doesn't hurt, but I find the easiest way is to start by using models and visuals to explain WHY we are getting the numbers we get and then moving on to doing practice problems without the models. Giving students multiple ways to visualize and understand the material increases their chances of understanding and remembering the material. It is important to find what works for them.
How do we solve a two step equation such as $$3x-1=11$$?
When solving equations we are looking to get x all by itself. To do this we must do the inverse operations to "undo" each of the operations we are doing on x. Inverse means opposite so for example, addition and subtraction are inverses and multiplication and division are inverses. To solve the above problem you would first want to "undo" the subtract 1 by adding one to both sides. We must do the same operation to both sides to keep the equation balanced. Adding one on the left leaves 3x behind and 12 on the other side. The last step is to undo the times 3 by dividing both sides by 3. On the left side we are left with x and on the right side we are left with 4, so x=4.
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