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>
Answer:
we conclude that:

The graph is also attached below.
Step-by-step explanation:
Given the inequality expression

simplify

Add -1 to all parts

simplify

Divide all parts by -4


Thus, we conclude that:

The graph is also attached below.
4 hours and 10 minutes have elapsed.
Answer:
Identifying and Writing Equivalent Rates
Ratios compare two quantities. A rate is a type of ratio that compares two quantities that have different units of measurement. The word “per” is often used to describe rates.
Rates can be written as fractions. The first quantity is the numerator and the second quantity is the denominator. Different rates that have the same value are equivalent rates. You can find an equivalent rate the same way you find equivalent ratios—divide or multiply the numerator and the denominator by the same number.
Step-by-step explanation:
Answer:
<h3>The Equivalent of 4 (4a+b) is </h3>
Step-by-step explanation:
<u>step</u><u> </u><u>1</u><u>.</u>
<u>4</u><u> </u><u>(</u><u>4a</u><u> </u><u>+</u><u>b</u><u>)</u>
<u>step</u><u> </u><u>2</u><u>.</u><u> </u><u>multiple</u><u> </u><u>the</u><u> </u><u>whole</u><u> </u><u>bracket</u><u> </u><u>by</u><u> </u><u>4</u>
<u>(</u><u>4</u><u>×</u><u> </u><u>4a</u><u> </u><u>+</u><u> </u><u>4</u><u>×</u><u>5</u><u>)</u>
<u>16a</u><u> </u><u>+</u><u> </u><u>20</u>