higgsb

3x-9 = -x+7  --> add x to both sides

4x-9 = 7       --> add 9 to both sides

4x = 16        --> divide both sides by 4

x = 4

I don't understand what you are asking for in question 3, so I'm going to skip it for now...

4.(x² + 1) - (3x² + 4x - 1)    --> remove parenthesis

x^2 + 1 - 3x^2 - 4x + 1       --> combine like terms

-2x^2 - 4x + 2

2. (a² + a - 1) - (3a² - 2a + 5)  --> remove parenthesis 

a^2 + a - 1 - 3a^2 + 2a - 5      --> combine like terms

3a - 2a^2 - 6                           --> rewrite into standard form for a quadratic (ax^2 + bx + c)

-2a^2 + 3a - 6

1. (3x² + 2xy + 7) - (6x² - 4xy + 3) --> remove parenthesis

3x^2 + 2xy + 7 - 6x^2 + 4xy - 3     --> combine like terms

6xy - 3x^2 + 4                               --> rewrite in standard form of a quadratic (ax^2+bx+c)

-3x^2 + 6yx + 4

Since you are multiplying 86 by 97 right after you are dividing 86 by 97, and multiplication and division are opposite opertations, they cancel each other out, and your answer is 86. 

The domain of a function f(x) is the values that x can be. 

If you want to know how to find the domain of a function, this website gives some examples: 

http://www.coolmath.com/algebra/15-functions/06-finding-the-domain-01

p = perimiter

h = height

w = width

You have the inequality p<200, and the equation 2w+2h = p.

You can subsitute 2w+2h for p, so you get a new inequatlity of 2w+2h<200.

Since we know that w is 36, we can plug that value in: 2*36+2h<200  -->  72+2h<200.

Now we can solve this inequality for h: 

72+2h<200  -->  subtract 72 from both sides

2h<128        --> divide both sides by 2

h<64            --> Our answer is that the height of the frame must be less than 64 inches. 

−10 + 7𝑥 + 24 − 2  ---> combine like terms (add the numbers)

7x + 12 

If you have a set of numbers, the range is the difference between the largest number and the smallest number.

(Example - If your set was {3, 2, 7, 11, 12}, your range would be the largest number (12) - the smallest number (2).

[12-2 = 10, which is the range.]

1.05-z=1.65  --> subtract 1.05 from both sides

-z = 0.6 --> multiple both sides by -1

z = -0.6