1 Programa P.A.L.M. Microdisector Laser Tutorial 3/3 Tutorial 3/3 BARRA GENERAL BARRA GENERAL.
Tutorial 3 Mth3200
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MTH3200 Tutorial 3 1. Solve: a) 3 2 4 1 x x + < - e) 10 3 2 16 x - ≥ + >- i) 2 5 4 3 - = + x x b) 4 1 3 x ≤ - f) 3 2 (5 3) 0 (8 25) x x - ≤ - j) 5 4 3 - < x x c) 2 2 4 10 x x >- - g) 3 1 2 1 x x + ≤ - k) 3 6 = - x d) 4 3 4 5 x - - ≤ < - h) 4 2 3 x x + > - l) 6 1 3 1 x x + ≥ - 2. Write the solution for each of the following inequality in interval form and then sketch the solution on a number line. a) 2 6 16 8 x x + + ≤ d) 4 5 1 9 2 x - < < - g) 13 2 3 5 x - ≤- + <- b) 6 30 x x + >- e) 1 3 2 6 x x ≤ - + h) 4 7 2 5 3 x x + ≤ + - c) 5 1 3 x x - - > + f) 15 4 3 7 < - ≤ x i) 3 (9 11)(2 7) 0 (3 8) x x x - + > - 3. Let , ,, , ab cd ∈ then prove: a) ( ) ( ) a b c a b c + - = + - e) a b a b + ≤ + b) If ac bc = , and 0 c ≠ , then a b = f) a b a b - ≤ - c) a a a b b b - = =- - ( 0) b ≠ g) a b c - < iff b c a b c - < < + d) If , a d b = ( 0) b ≠ then a bd = h) ( ) ( ) ( ) c a c a - + =- +-
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Tutorial MTH3200
Transcript of Tutorial 3 Mth3200
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MTH3200
Tutorial 3
1. Solve:
a) 3 2
41
x
x
+ i) 2543 =+ xx
b) 4
13 x
f) 3
2
(5 3)0
(8 25)
x
x
j) 543 < xx
c) 2
24 10
x
x>
g) 3 1
21
x
x
+
k) 36 =x
d) 4
3 45
x
l) 6 1
31
x
x
+
2. Write the solution for each of the following inequality in interval form and then sketch the solution on a number line.
a) 2 6 16 8x x+ + d) 4 5
1 92
x < e) 1 3
2 6x x
+
h) 4 7
2 53
xx
+ +
c) 5
13
x
x
>
+
f) 15437
3. Let , , , ,a b c d then prove:
a) ( ) ( )a b c a b c+ = + e) a b a b+ +
b) If ac bc= , and 0c , then a b= f) a b a b
c) a a a
b b b
= =
( 0)b g) a b c < iff b c a b c < < +
d) If ,a
db
= ( 0)b then a bd= h) ( ) ( ) ( )c a c a + = +