Question

How do you solve `-\frac { 6} { 5} - \frac { 1} { 2} u = - \frac { 5} { 7}`?

Answer 1

Isolate the variable on one side of the equation, and all of the constants on the other. The answer will be `u= -34/35`

Explanation:

When solving an equation of this sort, one must Isolate the variable from the constant terms. I will also multiply both sides by -1 for ease of use. Thus:
`-6/5 -1/2u=-5/7 -> 6/5 +1/2u = 5/7 -> 1/2u = 5/7 - 6/5`

If we wish to simplify here, we will find the lowest common denominator of 5/7 and -6/5. Since both are prime, this lowest common denominator will be the product of the denominators we have, 35. In order to get 5/7 in terms of a denominator of 35, we must multiply top and bottom by 5, and to get the same denominator for our -6/5 we multiply top and bottom by 7.

`1/2u=5/7 -6/5 = 25/35 - 42/35 = -17/35 -> u = -34/35`

Answer 2

`u=-34/35`

Explanation:

Everything is negative so to make everything positive multiply both sides by (-1) giving:

`6/5+1/2u=5/7`

Notice that all of the denominators will divide exactly into 70.

`color(green)([6/5color(red)(xx1)]color(white)("d.")+color(white)("d")[u/2color(red)(xx1)]color(white)("d")=[5/7color(red)(xx1)])`

`color(green)([6/5color(red)(xx14/14)]+[u/2color(red)(xx35/35)]=[5/7color(red)(xx10/10)])`

`84/70+(35u)/70=50/70`

Multiply everything by 70

`84+35u=50`

Subtract 84 from both sides

`35u=-34`

Divide both sides by 35

`u=-34/35`