Questions on Algebra: Inverse operations for addition and multiplication, reciprocals answered by real tutors!

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x/3+5=15

x/3=15-5

x/3=10

x=10*3

x=30

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Your answer is correct, but be careful. A common mistake that beginning students make in doing maths is to try to do too much in their heads. If they make a mistake it can be difficult to find and correct. Here's the way that I would have worked the problem step-by-step, and you can track through it. (You appear to have done each of these steps in working the problem):
.
Given to solve:
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Step 1: Do the distributed math by multiplying -3 times each of the two terms in the parentheses to get:
.

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Step 2: Combine the +5 and the +9 on the left side and you have:
.

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Step 3: To get closer to the solution, recognize that you need to get all the unknown terms gathered on one side of the equation and all of the numbers gathered together on the other side. So you need to get rid of the +14 on the left side (leaving only the -6b on the left side). To get rid of the +14 on the left side, subtract -14 from both sides and the equation becomes:
.

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Step 4: Notice on the left side that the +14 and the -14 combine to zero. So they disappear. And on the right side the -4 and the -14 combine to -18. This makes the equation now become:
.

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Step 5: Finally, solve for b by dividing both sides by -6 which is the multiplier of b. This is written as:
.

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Step 6: On the left side the -6 in the denominator cancels with the -6 in the numerator and you are left with just b. On the right side the -6 in the denominator divides into the -18 in the numerator 3 times. And the entire equation is reduced to the answer of:
.

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Some comments on the process you documented. First, I'm not sure why you switched from the unknown variable "b" to a new unknown variable "x". You should just leave it as b because you are being asked to solve for b, not for x. Second, I'm not sure where the extra 6x in the left hand numerator came from when you wrote:
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-6x6x/6=-18/-6
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And also, where did the minus sign in the denominator on the left side go to? You seem to be a little confused in what you are doing in your process at this point, but you did get the correct answer of +3. Look at my Step 5 to see how to do this step. In the format that you used, you should have documented this just as:
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-6x/-6 = -18/-6
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I hope this helps you to understand a little more about solving equations. You seem to have the general idea, and just need to be careful with what you are doing. Keep up the good work and good luck!
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h + (-11) = -18


h - 11 = -18


h - 11 + 11= -18+11


h = -7
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You can put this solution on YOUR website!













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If you need more help, email me at jim_thompson5910@hotmail.com

Also, please consider visiting my website: http://www.freewebs.com/jimthompson5910/home.html and making a donation. Thank you

Jim
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Sometimes multiple choice questions are best solved by trying out each
choice to find out which one works:

Notice what is different about the notation f(x) and the notation f(g(x))

If you replace the x in f(x), by g(x), you get f(g(x))

So what we do with the right sides of f(x) and g(x) is the same. We replace
x in the right side of the f(x) equation by the ENTIRE RIGHT SIDE of the
g(x) equation.

 

if f(g(x)) = 6x³, what are possibilities for f,g?

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Let's see if (a) is the correct answer:

a) f(x) = 6x, g(x) = x²

Let's substitute the right side of the g(x) equation for x
in the f(x) equation:

f(g(x)) = 6(x²) = 6x² 

So (a) is not correct.

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Let's see if (b) is the correct answer:

b) f(x) = x², g(x) = 6x

Let's substitute the right side of the g(x) equation for x
in the f(x) equation:

f(g(x)) = (6x)² = 36x²

So (b) is not correct.

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Let's see if (c) is the correct answer:

c) f(x) = 2x, g(x) = 3x³

Let's substitute the right side of the g(x) equation for x
in the f(x) equation:

f(g(x)) = 2(3x³) = 6x³

So (c) is the correct choice.  

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We have the answer but let's follow through and see why (d) isn't correct:

---------------------------------

Let's see if (d) is the correct answer:

d) f(x) = 3x^3, g(x) = 2x

Let's substitute the right side of the g(x) equation for x
in the f(x) equation:

f(g(x)) = 3(2x)³ = 3·2³x³ = 3·8x³ = 24x³

So (d) is not correct.

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Answer (c)


Edwin