# Thread: algebra equation

1. ## algebra equation

Hello all, I'm currently in an online math course do not understand any of these review questions. We were pretty much just told to do these without any guidance, example, or review. I was wondering if someone could help me with these problems!

1. 9(3x+2)-10x=12x-7<--solve for x

2. One number is 7 less than another. If four times the smaller number plus 2 times the larger number is 62, find the two numbers.

3. Solve each literal equation for the indicated variable:

I-Prt (for r)
A=1/2 (h(B+b) (for B)

4. Solve each literal equation for the indicated variable:

V=LWH (for H)
D=(c-s)/n (for s)

If someone would be able to solve them and explain a little bit about them I would appreciate it, these are the only questions i've been having trouble on throughout the night

2. Originally Posted by cstevens2005
...

1. 9(3x+2)-10x=12x-7<--solve for x
to transform the equation you are allowed to add, to subtract, to multiply and to divide both sides of the equation (by) the same term:

$\displaystyle 9(3x+2)-10x=12x-7$ ........ Expand the brackets:
$\displaystyle 27x+18-10x=12x-7$ ........ Collect like terms: x at the LHS, the constants at the RHS:
$\displaystyle 5x = -25$ ........ Divide by the leading coefficient of x:
$\displaystyle \boxed{x=-5}$ ........ Solution. To control your work plug in this value into the original equation and check if you get a true statement.

The questions 3. and 4. have to be done in exactly the same way.

2. One number is 7 less than another. If four times the smaller number plus 2 times the larger number is 62, find the two numbers.

...
1. You are looking for 2 numbers:
first number: x
second number: x-7

2. Translate the sentence intoan equation:

$\displaystyle 4\cdot(x-7) + 2\cdot x = 62$

Use the transformations I've used above: ........ Expand the brackets:

$\displaystyle 4x-28+2x = 62$ ........ Collect like terms: x at the LHS, the constants at the RHS:

$\displaystyle 6x = 90$ ........ Divide by the leading coefficient of x:

$\displaystyle \boxed{x = 15}$ ........ Solution. To control your work plug in this value into the original equation and check if you get a true statement.