Answer:
<em>a) 3<x<8</em>
<em>b) -4<x<-2</em>
<em>c) -6<x<5</em>
<em>d) -21/4 < x-8/3</em>
<em>e) 0<x<7</em>
Step-by-step explanation:
Given the following inequalities
a) x > 3, 2x - 3 < 15
Solve 2x - 3 < 15
2x < 15+3
2x<18
x<18/2
x<8
Combine x>3 and x<8
If x>3, then 3<x
On combining, we have:
3<x<8
b) For the inequalities 25 > 1 - 6x, 1 > 3x + 7
25 > 1 - 6x
25-1>-6x
24>-6x
Divide through by -6:
24/-6 > -6x/-6
-4 <x
For the inequality 1 > 3x + 7
1-7>3x
-6>3x
-6/3 > 3x/3
-2 > x
x < -2
Combining both results i.e -4 <x and x < -2, we will have:
-4<x<-2
c) For the inequalities 2x - 7<3< 27 + 4x
On splitting:
2x - 7<3 and 3< 27 + 4x
2x < 3+7
2x<10
x<5
Also for 3< 27 + 4x
3-27<4x
-24<4x
-24/4 < 4x/4
-6<x
Combining both solutions i.e x<5 and -6<x will give;
<em>-6<x<5</em>
d) For the inequalities 3x + 8 <0 < 21 + 4x
3x + 8 <0
3x < -8
x < -8/3
Also for 0 < 21 + 4x
0-21<4x
-21<4x
-21/4 < 4x/4
-21/4 < x
Combining -21/4 < x and x < -8/3 will give;
<em>-21/4 < x-8/3</em>
<em></em>
e) For the inequalities 5x - 36 < -1 < 2x – 1
Split:
5x - 36 < -1
5x < -1+36
5x<35
5x/5 < 35/5
x < 7
For the expression -1 < 2x – 1
-1+1 < 2x
0 < 2x
0<x
Combining both inequalities 0<x and x < 7 will give:
<em>0<x<7</em>
