solve the following inequalities (a) 3x-5< 9 + x (b) 6 -5y >/ 17. In each case give the largest?

Question

interger which satisfies the inequality.

2. FInd all the solutions of the following equations:
a) 3x-7=5-x
b) 3(y-2)=2 (7-4y)
b) 5-3b /3 =2b + 1/5

3. Mr Jones has the option of having the gas supplied to his home by one of two companies. Both Companies have a fixed standing charge per quarter and charge a fixed rate for each unit of gas consumed.
Company A is mr Jones current supplier. His bills for te last two quarters have been $122.50 and $158.50 for 250 and 330 units of gas respectively. Company B has the standing charge of $17.00 and charges 43 cents for each unit of gas consumed.
(a) For both companies, find an expression for the cost, C, of a quarterly bill in terms of the number of units,u,of gas consumed.
(b) Determine how many units of gas Mr. Jones would have to consume per quarter to make it worth his while charging his gas supplier.

4.Draw the curve y=x2 - x-6 for values of x between -4 and 5.Henc find the smallest value y takes and solve inequality x2-x-6<0

Answer 1

1.
a) 3x-5<9
Add 5 to both sides:
3x<14
Divde by 3:
x<(14/3)
The largest integer is then:
4.
b) I guess you mean
6-5y≥17
In which case you subtract 6 from each side:
-5y≥11
And divide by -5;
y≥(-11/5)
11/5 is about 2.2, so the largets integer is -3

2.
a)
3x-7=5-x
Add 7 and x to each side to get:
4x=12
Divide by 4 to get:
x=3

b)
3(y-2)=2 (7-4y)
Multiply to remove parentheses:
3y-6=14-8y
Add 8 and 8y to each side to get:
11y=20
Divide by 11 to get:
y=11/20
Then get out the calculator.

c)
5-3b /3 =2b + 1/5
There are two ways to look at this:
(5-3b)/3=2b+1/5
OR
5-(3b/3)=2b+1/5
So I can't help you here.

3.
Cost of company A:
C(u)=10+.45u
Cost of company B:
C(u)=17+.43u
By setting u=0 you can see that company A is cheaper.
Both equations are linear, so to find when company B is cheaper, set the two equations equal to each other:
10+.45u=17+.43u
subtract 10 and .43u from each side to get:
.2u=7
Divide by .2 to get:
u=35
The gas will be cheaper after 35 units.

4.
Can't draw graphs online, so I can't do this one.

Answer 2

1.(a). x < 7
(b). x < -23/5

2.(a). x=3
(b). y=20/11
(c). 5=b

3.(A). OMIT
(b). 35 units

4. My Computer wont let me draw the curve but it would be 4.

Answer 3

do your own homework