1.)
Break the equations in hafe
So lets do the first hafe of the number 1: -9x<18 (make sure u put the line underneath < )
multiply both sides by -1 9reverse the inequality
(-9x)(-1)> 18(-1)
simplify
9x> -18
divide both sides by 9
9x/9 > -18/9
Answer: x > -2
Second part of the equation:
x+6<0
subtract 6 from both sides
x+6-6<0-6
Answer: x< -6
2.) first part: -6<2(g-3)<2
-9< 2(g-3)
switch sides
2(g-3)-6
Divide both sides by 2
2(g-3)/2 > -6/2
simply g-3>-3
Add 3 to both sides
g-3+3>-3+3
simply: g>0
2(g-3)<2
Divide both sides by 2
2(g-3)/2 < 2/2
simply
g-3 < 1
add 3 to both sides
g-3+3 < 1+3
Simply
g < 4
(g > 0) and g < 4
combine the ranges
0 < g < 4
Second Part: 4<3-g<9
4< 3 -g
Add g to both sides 4+g<-g +g
simply
4+g<3
Subtract 4 to both sides
4+g-4<3-4
Simply
g<-1
(g<-1) and (g>-6)
combine the ranges
-6 < g < -1
3.)
-9>2/3y - 11
switch sides
2/3y- 11 < -9
Add 11 to both sides
2/3y -11 +11 < -9 + 11
Simply
2/3y < 2
Multiply both sides by 3
3 x 2/3y < 2 x 3
Simply
2y < 6
Divide both sides by 2
2y/2 < 6/2
Simply
y < 3
2/3y -11 > (the line underneath the >) -15
Add 11 to both sides
2/3y - 11+11 > -15+11
simply
2/3y > -4
Multiply both sides by 3
3 x 2/3y > 3(-4)
simply
2y > -12
Divide both sides by 2
2y/2 > -12 / 2
simply
2y/2
Divide the number 2/2 = 1
=y
-12 / 2 Apply the fraction rule -a/b= -a/-b
-12/-2
Divide the number 12/2 = 6
= -6
y > -6
y> -6
(y<3) and (y>-6)
Combine the ranges
-6<y<3
4.
solve 11, 2x+5/ 5
Switch dies 2x+5/5 > 11
Multiply both sides by 5
5(2x+5)/5 > 11 x 5
Simply
2x + 5 > 55
Subtract 5 by both sides
2x +5 -5 > 55-5
Simply
2x > 50
Divide both sides by 2
2x/2 > 50/ 2
x>25
2x+5/5 < 13
Multiply both sides by 5
5(2x+5)/5 < 13 x 5
Simply
2x + 5 < 65
Subtract 5 from both sides
2x +5 -5 < 65 -5
Simply most of the( <) have a line underneath but i dont know how to do that so your gonna have to figure that out by looking at the problem.
2x < 60
Divide both sides by 2
2x/2 < 60/2
Simply
x< 30
x > 25 and x (<) ( this arrow does have a line) 30
Combine the ranges
25< x (<)-(line underneath) 30
