Question 206626
PROBLEM 1
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5/8X + 1/16X= 5/16 + X   The solution is X= 1/32
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if i understand the problem correctly, your equation is:
{{{5/(8x) + 1/(16x) = 5/16 + x}}}
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i could not verify your answer as correct.
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i would have solved as follows:
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{{{5/(8x) + 1/(16x) = 5/16 + x}}}
multiply both sides of the equation by 16x to get:
{{{10 + 1 = 5x + 16x^2}}} which becomes:
{{{11 = 5x + 16x^2}}} which becomes:
{{{16x^2 + 5x - 11 = 0}}}
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i used the quadratic formula to get a solution of:
x = -1 or x = .6875
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substituting in the original equation of {{{5/(8x) + 1/(16x) = 5/16 + x}}} should confirm the answer as correct.
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if we let x = -1, then {{{5/(8x) + 1/(16x) = 5/16 + x}}} becomes {{{5/(8*(-1)) + 1/(16*(-1)) = 5/16 + (-1)}}}
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This becomes -(5/8) - (1/16) = (5/16) - 1
which becomes -11/16 = -11/16 confirming x = -1 is correct.
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if we let x = .6875, then {{{5/(8x) + 1/(16x) = 5/16 + x}}} becomes {{{5/(5.5) + 1/(11) = 5/16 + .6875}}}
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This becomes .90909090909... + .0909090909091... = .3125 + .6875
which becomes 1 = 1 confirming x = .6875 is also correct.
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a graph of this equation would look like this:
{{{graph(600,600,-5,5,-100,100,16x^2+5x-11)}}}
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an alternative interpretation of this problem would be:
{{{(5/8)*x + (1/16)*x = 5/16 + x}}}
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i would have solved as follows:
multiply both sides of this equation by 16 to get:
{{{10x + x = 5 + 16x}}} which becomes:
11x = 5 + 16x
subtract 11x from both sides and subtract 5 from both sides to get:
5x = -5
divide both sides by 5 to get:
x = -1
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substitute in the original equation of 11x = 5 + 16x gets -11 = -11 confirming the answer is correct.
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PROBLEM 2
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3(w-5)=6  W=___  ( I came up with W= 7) 
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this looks good.
substituting in your original equation we get:
3*(7-5) = 6
which becomes 3*2 = 6 which becomes 6 = 6 which means w = 7 is good.
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PROBLEM 3
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11X = -99  the solution is X=-9  (Is this correct)
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this also looks good.
substituting in your original equation we get:
11*(-9) = -99 which becomes -99 = -99 which means x = -9 is good.
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