This equation has some nested grouping symbols on the left-hand side. As usual, I'll simplify from the inside out. I'll start by inserting the "understood" 1 in front of that innermost set of parentheses:
3 + 2[4x – (4 + 3x)] = –1
3 + 2[4x – 1(4 + 3x)] = –1
3 + 2[4x – 1(4) – 1(3x)] = –1
3 + 2[4x – 4 – 3x] = –1
3 + 2[1x – 4] = –1
3 + 2[1x] + 2[–4] = –1
3 + 2x – 8 = –1
2x + 3 – 8 = –1
2x – 5 = –1
2x – 5 + 5 = –1 + 5
2x = 4
x = 2
It is not required that you write out this many steps; once you get comfortable with the process, you'll probably do a lot of this in your head. But until you reach that comfort zone, you should write things out at least this clearly and completely.
Always remember, by the way, that you can check your answers in "solving" problems by plugging the numerical answer back in to the original equation. In this case, the variable is only in terms on the left-hand side (LHS) of the equation; my "check" (that is, my evaluation at the solution value) looks like this:
LHS: 3 + 2[4x – (4 + 3x)]:
3 + 2[4(2) – (4 + 3(2))]
3 + 2[8 – (4 + 6)]
3 + 2[8 – (10)]
3 + 2[–2]
3 – 4
–1
Since this is what I was supposed to get for the right-hand side (that is, I've shown that the LHS is equal to the RHS), my solution value was correct.
X= # of adults
y= # of children
1326= 6x + 4y
289= x + y
We are going to do substitution.
x = 289-y
1326= 6(289-y) + 4y
1326= 1734 -6y + 4y
1326= 1734 + -2y
-408= -2y
204 = y
Since we now have a value for y, we should plug that back into the equation we got the x value from to find the actual numerical value of x.
289= x + y
289= x + 204
85= x
In conclusion, 85 adults and 204 adults went to the swimming pool.
Answer:
When simplified they all are 1/5
So yes they are proportional
Answer:
186 books with the 55% increase
Step-by-step explanation:
120 times 55% increase = 66 more in increase
Now take the increase and add it to the original amount of books to get the number of books with the increase
66 + 120 = 186
The answer to the question is 4
