1. commutative property states that : a + b = b + a
2. 3x - 5 = 5x - 17 -- add 5 to both sides
3x = 5x - 17 + 5 -- subtract 5x from both sides
3x - 5x = -17 + 5 -- combine like terms
-2x = -12 -- divide both sides by -2
x = 6
3. slope formula : slope = (y2 - y1) / (x2 - x1)
(3,-1) x1 = 3 and y1 = -1
(-2,-5) x2 = -2 and y2 = -5
now we sub
slope = ((-5 - (-1)) / (-2 -3)
slope = (-5 + 1) / -5
slope = -4/-5
slope = 4/5
4. x = first integer
x + 2 = 2nd integer
x + x + 2 = 80 -- combine like terms
2x + 2 = 80 -- subtract 2 from both sides
2x = 80 - 2
2x = 78 -- divide both sides by 2
x = 39 <== this is the smallest number
x + 2 = 41
5. p = 1/2g - 3
6. The union of two sets is all the numbers in both sets, no need to copy the same number more then once. Answer is : (1,2,3,4,5,6,8,10)
7. 2x + 3y <= 6 -- put in y = mx + b form
3y <= -2x + 6
y <= -2/3x + 2
In y = mx + b form, the y intercept is in the b position. So the y intercept is (0,2)
To find the x intercept, sub in 0 for y (change inequality sign to equal sign)
2x + 3y = 6
2x + 3(0) = 6
2x = 6
x = 3
x intercept is (3,0)
So plot your points (3,0) and (0,2)
Connect the points with a solid line because there is an equal sign in there.
Shade below the line because it is less then.
8. 3x + 6y = 8
6y = -3x + 8
y = -1/2x + 4/3
y = 2x - 8
Perpendicular lines have negative reciprocal slope. All that means is " flip " the slope and change the sign. The slope in these equations are -1/2 and 2. These are negative reciprocals of each other.
9. 7x + 3y - 2 + 6x + 1 + y^2
y^2 + 3y + 13x - 1
10. (0,6) x1 = 0 and y1 = 6
(3,0) x2 = 3 and y2 = 0
slope(m) = (y2 - y1) / (x2 - x1)
slope(m) = (0 - 6) / (3 - 0)
slope(m) = -6/3
slope(m) = -2
y = mx + b
(0,6) x = 0 and y = 6
6 = 0(-2) + b
6 = b
your equation is : y = -2x + 6 (slope intercept form)
2x + y = 6 (standard form)
11. x + y = 5 -- put this in y = mx + b form, and the m position is your slope
y = -x + 5 (-x is the same as -1x) so your slope is -1
12. 4y = 8x - 3 -- put in y = mx + b form, and the b stands for the y intercept
y = 8/4x - 3/4
y = 2x - 3/4 (the y intercept is -3/4
13. |a| + b --- (a = -1.4 and b = -2.7)
absolute values, whether they have a negative or not, they are always positive
|a| + b
|-1.4 | + (-2.7)
1.4 - 2.7 = -1.3 <== your answer
14. I cannot see the problem
15. -4 < 2t <= 2 --- divide everything by 2
-2 < t <= 1
open circle on -2, closed circle on 1, shading in between
16. x + 2y = -9 ---> x = -2y - 9
now sub -2y - 9 in for x in the other equation
4x - 2y = 14
4(-2y - 9) - 2y = 14 -- distribute through the parenthesis
-8y - 36 - 2y = 14 -- add 36 to both sides
-8y - 2y = 14 + 36 combine like terms
-10y = 50 -- divide by -10
y = -5
now sub -5 in for y in either of the original equations
x + 2y = -9
x + 2(-5) = -9
x - 10 = -9
x = -9 + 10
x = 1
answer : x = 1 and y = -5 or (1,-5)
I was really bored so I thought I would just help out :)
