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Orlov [11]
3 years ago
6

How many solutions are there to the equation below 6×+30+4×=10(×+3)

Mathematics
1 answer:
Elena-2011 [213]3 years ago
7 0

Answer:

Infinite many solutions. Any x-value can satisfy the equation.

Step-by-step explanation:

Let's work on simplifying the equation a little to investigate which x-values satisfy it. Start by combining like terms on the left side (6x +4x=10x),

then distribute the factor "10" into the binomial (x+10), obtaining 10x +30.

Now we have the same expression on the left and the right of the equal sign:

10x +30=10x+30. We may subtract 30 from both sides, and obtain 10x=10x, and at this point divide by 10 both sides, and we obtain: x=x

The process is shown below.

6x+30+4x=10(x+3)\\6x+4x+30=10x+30\\10x+30=10x+30\\10x=10x\\x=x

x=x is an equation that is verified by absolutely ANY x value on the number line, and there are infinite x-values in the number line.

Therefore there are infinite many solutions to this equation (any x-value will satisfy it).

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We can write this in math as x+y+z=104, x=y-6, and z=3y

Because we already know what x and z are in terms of y, we can substitute our values for x and z into the first equation. This now looks like (y-6) + y + (3y) = 104. Now we can simplify our equation to find our value for y.

y-6 + y + 3y = 104 simplifies to 5y - 6 = 104, then 5y=110, and finally y=22.

Now that we know our value for y we can find our values for x and z by substituting our value for y into the other two equations.

The second equation x = y-6 can be simplified as x = 22 - 6 and further simplified as x = 16.

The third equation z = 3y can be written as z = 3(22) or z = 66.

Our three numbers are 16, 22, and 66. Hope this helps you!
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