Explanation:
that is so simple. we only need to use the given value of the variable at every location of the variable and then calculate and compare both sides of the inequality.
if the inequality is true, then the given value was a solution. if not, not.
that is all there is to it.
9.
r = 2
2 + 4 > 8
6 > 8
false, r = 2 is NOT a solution.
10.
x = - 3
5 - -3 < 8
5 + 3 < 8
8 < 8
false, x = -3 is NOT a solution.
11.
s = -6
3×-6 <= 19
-18 <= 19
true, s = -6 is a solution.
12.
y = 7
17 >= 2×7
17 >= 14
true, y = 7 is a solution.
13.
x = 3
-1 > -3/2 = -1 ½
true, x = 3 is a solution. please remember, everything to the left of a number on the number line is smaller than that number.
14.
z = 2
4/2 >= 3
2 >= 3
false, z = 2 is NOT a solution.
15.
z = 5
20 <= 10/(2×5) + 20
20 <= 10/10 + 20
20 <= 1 + 20
20 <= 21
true, z = 5 is a solution
we could have simplified :
20 <= 10/(2z) + 20
0 <= 10/(2z)
0 <= (10/2)×1/z
0 <= 1/z
this is true for any z > 0.
16.
m = 8
3×8/6 - 2 > 3
24/6 - 2 > 3
4 - 2 > 3
2 > 3
false, m = 8 is NOT a solution.
17.
n = -2.9
10.4 >= -2×-2.9 + 4.6 = 5.8 + 4.6
10.4 >= 10.4
true, n = -2.9 is a solution.
18.
q = ⅚
-5×⅚ - 7/4 + 8×⅚ < ⅝
-5 + 8 = 3
therefore, -5q + 8q = 3q
3×⅚ - 7/4 < ⅝
5/2 - 7/4 < ⅝
now, let's bring everything to ⅛ :
20/8 - 14/8 < ⅝
6/8 < 5/8
false, q = ⅚ is NOT a solution.