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:
x = 10
Step-by-step explanation:
We know that is a right angle which is 90 degrees.
we know one angle is 30 degrees.
So take 90- 30 = 60
now we solve for 6x
6*10 = 60 and 60+30=90
x = 10
Answer:
a
Step-by-step explanation:
Domain means the change in x.
so the domain will be which values of x the fn goes through.
you can see the black line goes from -9 to 2 in x values.
the -9 isn't filled in, but the 2 is. filled in means it will be with an equals instead of without.
so x is between -9 and 2, 2 is with equals -9 is without,
so the first one.
The last pair.
Because 2*4/3*4=8/12
Answer:
The answer to your question is Katie had 15 rocks and Oliver 45 rocks.
Step-by-step explanation:
Conditions
Katie has x amount of rocks
Oliver has 3x amount of rocks
The final amount of rocks
Oliver = 3x + 75
Katie = x + 105
Now, they have the same amount of rocks, then we can equal both equations
3x + 75 = x + 105
Solve for x
3x - x = 105 - 75
2x = 30
x = 30/2
x = 15
Conclusions
At first Katie had 15 rocks and Oliver had 3(15) = 45 rocks