Solve for x (3x + 1)/7 - (3x + 5)/3 = (x+3)/21.

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giorgiana1976's profile pic

giorgiana1976 | College Teacher | (Level 3) Valedictorian

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Before computing x, we'll have to calculate the least common denominator of the 3 ratios.

LCD = 3*7

LCD = 21

Now, we'll multiply the first ratio by 3 and the second ratio by 7. The 3rd ratio has the denominator 21, so it won't be multiplied.

We'll re-write the equation, all 3 quotients having the denominator 21;

3(3x + 1) - 7(3x + 5) = (x+3)

We'll remove the brackets:

9x + 3 - 21x - 35 = x + 3

We'll move all terms to one side:

9x + 3 - 21x - 35 - x - 3 = 0

We'll combine and eliminate like terms:

-13x = 0

We'll divide by -13:

x = 0

The solution of the equation is x = 0.

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neela | High School Teacher | (Level 3) Valedictorian

Posted on

To solve for x (3x + 1)/7 - (3x + 5)/3 = (x+3)/21..

This is a linear equation in one variable x. So we solve x by isolating x 's on one side and numbers on the other side by way of operation of adding equals to both sides , subtractiing equals from both sides , multiplying or dividing  both sides by equals (but never by multiplying or dividing by zero).

First we multiply by 21 to get rid of deminators:

21 (3x + 1)/7 - 21(3x + 5)/3 = 21(x+3)/21.

3(3x+1) -7(3x+5) =x+3.

9x+3 -21x-35 = x+3 .

(9x-21x) +3-35 = x+3.

-12x - 32 = x+3.

-12x -x = 32+3.

-13 x = 35.

x = 35/-13.

x = -35/13.

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