1) State whether the following pairs of fractions are equivalent or not :
1 answer:
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Lets make the graph of our systems of equations:
The blue line correspond to the equation x-y=3 and the red one correspond to 7x-y=-3. The lines intersect at point (-1,-4), then, the solution of the system is (-1,-4).
Answers:
The starting equation is (x+5)/3 = 7 which can be written as
The solution to this equation is x = 16
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Explanation:
Let x be a placeholder for some number. If we start off with some number and add on 5, then we go from x to x+5. The next thing we do is divide all of "x+5" all over 3 to get (x+5)/3 which can be written as . I'll use the first style of notation.
Set the expression (x+5)/3 equal to 7 and that leads us to the equation:
(x+5)/3 = 7
so this is the first part of the answer. Now onto the second part which is solving for x. We want to get x all by itself on its own side.
To do this, we follow the order of operations PEMDAS in reverse. So we undo division first by multiplying both sides by 3. Then we undo the addition of 5 by subtracting 5 from both sides
(x+5)/3 = 7
3*(x+5)/3 = 3*7 ...... multiply both sides by 3
x+5 = 21
x+5 - 5 = 21 - 5 ..... subtract 5 from both sides
x = 16
So the unknown mystery number is 16. As a check, note how adding 5 to 16 gets us 16+5 = 21, which if we divide by 3 we end up with 21/3 = 7 which is what we want. So the answer is confirmed.