Answer:
(c) III
Step-by-step explanation:
If you simplify the equations and the left side is identical to the right side, then there are an infinite number of solutions: the equation is true for all values of x.
Another way to simplify the equation is to subtract the right side from both sides. If that simplifies to 0 = 0, then there are an infinite number of solutions.
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<h3>I. </h3>
2x -6 -6x = 2 -4x . . . . eliminate parentheses
-4x -6 = -4x +2 . . . . no solutions (no value of x makes this true)
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<h3>II.</h3>
x +2 = 15x +10 +2x . . . . eliminate parentheses
x +2 = 17x +10 . . . . one solution (x=-1/2)
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<h3>III.</h3>
4 +6x = 6x +4 . . . . eliminate parentheses
6x +4 = 6x +4 . . . . infinite solutions
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<h3>IV.</h3>
6x +24 = 2x -4 . . . . eliminate parentheses; one solution (x=-7)
To determine the nth term, we must create a function.
f(n) = 1st term + common difference (n - 1)
n = term you are looking for
1st term = 1st number in the sequence
common difference = the difference between two consecutive numbers in the sequence.
based on the above sequence, the 1st term is 2, its common difference is 3.
f(n) = 2 + 3(n-1)
Assuming we are looking for the 5th term
f(5) = 2 + 3(5-1)
= 2 + 3(4)
= 2 + 12
f(5) = 14 as you can see in the above sequence 14 is the 5th term.
For any other value of the nth term, simply substitute n by the number of the term and solve the equation.
Let's make things easier by simplifying things.
y = 8 and x = 3 is more likely to be understood as a ratio. So for the rest of the answer, their relationship would be represented as y:x
Thus: y:x = 8:3
The problem would be finding y when x = 45
Let us proceed on using the previous equation and substitute x with 45 which would look like this:
y:45 = 8:3
Ratios can also be expressed as fractions which would make things more understandable and easy to solve. So the new form of our equation would be like this:
y/45 = 8/3
Then we proceed with a cross multiplication where the equation becomes like as what is shown below:
3y = 45 * 8
From there, you can solve it by multiplying 45 and 8 then dividing the product with 3 to get y
3y = 360
y = 120
Another way of looking at the problem, especially problems like these, is to take the whole question or statement as an equation. it would probably look like this:
y = 8 when x = 3 : y = ? when x = 45
This would make you understand what approach you can use to solve the given problem.