1. Ok well first you have to distribute. Remember this little saying PLEASE EXCUSE MY DEAR AUNT SALLY which stands for the order of operations-inside the parenthesis, exponents, multiply, divide, add, and subtract. But for this problem when you have a single number or letter outside of the parenthesis, you distribute that to everything inside the parenthesis.
For example: 2(3+4)=
Well, you can add 2+4 (from the please in the saying) and then multiply that answer by 2 or you can multiply the 3 and the 4 by 2 and then add them together. Try it-either way you come up with 14.
So to answer number 1: 3(x-8)=-2(x+6)
Distribute: 3x-24 = -2x + (-12)
**make sure you distribute that negative sign also!!!
Simplify: to simplify you get all of your variables on one side:
3x + 2x = 24 + 12
Because you add 2x to both sides to eliminate it from one side then you add 24 to both sides to eliminate it from the other side. Again simplify:
5x = 35
Now divide by 5 on both sides and x=7
2. -5x-12-3x= -18
If you want to get complicated you could divide the entire problem by a -1 to make all of the minuses pluses and the negative signs to go away. That concept use to confuse me so we will just work it out: Add 12 to both sides to get rid of it on the left:
-5x-3x = -18 + 12
Now add/subtract and remember your rules with negative numbers:
-8x = -6
And divide by -8 on both sides leaving x= 6/8 or 3/4 to simplify the fraction
3. t/2 + 5 = 4t + 4
First thing I would do is multiply the entire thing by 2. Remember you can do whatever you want to an equation as long as what you do to the left of the equals sign, you also do to right of the equals sign. So
2(t/2 + 5) = 2(4t + 4)
Remember the distribution we talked about in problem 1:
t + 10 = 8t +8
Now move the variables to one side and the numbers to the other:
10-8=8t-t ; 2= 7t
Divide by 7 on both sides and t=2/7
To substitute, you need to set every thing equal to one variable and then substitute that for that variable in the next equation.
1. 3x + 2y = 9 ; -10x +5y = -5
Take the second equation and divide both sides by 5:
1/5 (-10x + 5y) = 1/5(-5)
-2x + y = -1
Now isolate the y
y= 2x +1
Next, go back to the first equation and plug (2x +1) in for every "y"
3x +2(2x +1) = 9
Now distribute and solve
3x +4x +2 = 9 ; 7x +2 = 9 ; 7x = 7 ; x=1
Finally, go back to the other equation and plug 1 in for x to solve for y
-10x +5y = -5 ; -10(1) + 5y = -5 ; -10 + 5y = -5 ; 5y = 5 y=1
So x=1 and y=1
Try the other two on your own-I'm sure someone has posted answers.
For the quadratic formula, here is a little song it goes to the tune "Where is thumbkin"
Negative b, negative b, plus or minus square root, plus or minus square root, b squared minus 4ac, b squared minus 4ac all over 2a, all over 2a
Now a is the coefficient of the squared variable such as 4a^2 (a^2 means a squared) so the a in this case is 4
B is the one with a regular variable such as 4a; 4 would be the B
and C is the plain number-no variable.
So to use the quadraitic formula for 1.:
x^2 + 6x +9
It would be -6 plus or minus the square root of (6^2 - 4*1*9) all divided by (2*1)
So: -6 plus and/or minus square root (36-36) all divided by 2; so -6/2 or -3
2. 2x^2 -7x = -5
To use the quadratic formula the equation must be set equal to zero: 2x^2 -7x + 5 = 0
Now sing the song and set up the equations:
-(-7) plus or minus square root ((-7)^2-4*2*5) all divided by (2*2)
So to simplify 7 plus or minus sq root 49-40 all divided by 4
Simplify: 7 plus or minus sq root 9 all divided by 4
Simplify: 7 plus or minus 3 all divided by 4
Solve (7+3)/4 and (7-3)/4
So x=10/4 or 5/2 and 1
Again try the rest now and good luck!