To find equivalent inequalities you have to work the inequality given.
The first step is transpose on of sides to have an expression in one side and zero in the other side:
x - 6 x + 7
--------- ≥ --------
x + 5 x + 3
=>
x - 6 x + 7
--------- - -------- ≥ 0
x + 5 x + 3
=>
(x - 6) (x + 3) - (x + 7) (x + 5)
--------------------------------------- ≥ 0
(x + 5) (x + 3)
=>
x^2 - 3x - 18 - x^2 - 12x - 35
--------------------------------------- ≥ 0
(x + 5) (x + 3)
15x + 53
- ------------------- ≥ 0
(x + 5) (x + 3)
That is an equivalent inequality. Sure you can arrange it to find many other equivalent inequalities. That is why you should include the list of choices. Anyway from this point it should be pretty straigth to arrange the terms until making the equivalent as per the options.
Answer: The length of BC is 7
Step-by-step explanation: Assuming the lengths of the opposite sides of the quadrilateral are congruent, then
AB=DC and
AD=BC
Inputting the values of AB, DC and AD as given in the question:
x + 8 = 3x ...(1)
x + 3=? ...(2)
We have to solve for the value of x to get the actual lengths and thus ascertain BD.
From equation (1):
8 = 3x - x
8 = 2x
8/2 = x
Therefore, x = 4.
If x = 4 then equation(2) would be
4 + 3= 7.
Hence, the actual lengths of the quadrilateral are:
AB = 4 + 8. DC = 3(4)
=12. =12.
AD = 4 + 3. AD = BC
= 7. Therefore, BC = 7.
Hence, it is confirmed that quadrilateral ABCD is a parallelogram since both the opposite sides are proven to be congruent.
1 because 5÷3=1 and a remainder of 2 students.
Answer:
The equation of the straight line is 4x +y = 1
Step-by-step explanation:
<u><em>Step(i):-</em></u>
Given points are (-1,5) and ( 2,-7)
Slope of the line
slope of the line m = -4
<u><em>Step(ii):-</em></u>
The equation of the straight line passing through the point (-1,5) and having slope 'm' = -4
y - 5 = -4 ( x-(-1))
y -5 = -4 x -4
4 x + y -5 +4=0
4x +y -1 =0
<u><em>Final answer:-</em></u>
The equation of the straight line is 4x +y = 1
<u><em> </em></u>
Answer:
1.8
Step-by-step explanation:
1.8
