Question

How do you solve `-3/11=(5-h)/(h+1.4)`?

Answer 1

See a solution process below:

Explanation:

First, multiply each side of the equation by `color(red)(11)color(blue)((h + 1.4))` to eliminate the fractions while keeping the equation balanced. `color(red)(11)color(blue)((h + 1.4))` is the Lowest Common Denominator of the two fractions:

`color(red)(11)color(blue)((h + 1.4)) xx -3/11 = color(red)(11)color(blue)((h + 1.4)) xx(5 - h)/(h + 14.4)`

`cancel(color(red)(11))color(blue)((h + 1.4)) xx -3/color(red)(cancel(color(black)(11))) = color(red)(11)cancel(color(blue)((h + 1.4))) xx(5 - h)/color(blue)(cancel(color(black)(h + 14.4)))`

`color(blue)((h + 1.4))(-3) = color(red)(11)(5 - h)`

Next, expand the terms in parenthesis on both sides of the equation by multiplying each term within the parenthesis by the term outside the parethesis:

`(-3 xx color(blue)(h)) + (-3 xx color(blue)(1.4)) = (color(red)(11) xx 5) - (color(red)(11) xxh)`

`-3h - 4.2 = 55 - 11h`

Then, add `color(red)(4.2)` and `color(blue)(11h)` to each side of the equation to isolate the `h` term while keeping the equation balanced:

`-3h - 4.2 + color(red)(4.2) + color(blue)(11h) = 55 - 11h + color(red)(4.2) + color(blue)(11h)`

`-3h + color(blue)(11h) - 4.2 + color(red)(4.2) = 55 + color(red)(4.2) - 11h + color(blue)(11h)`

`(-3 + color(blue)(11))h - 0 = 59.2 - 0`

`8h = 59.2`

Now, divide each side of the equation by `color(red)(8)` to solve for `h` while keeping the equation balanced:

`(8h)/color(red)(8) = 59.2/color(red)(8)`

`(color(red)(cancel(color(black)(8)))h)/cancel(color(red)(8)) = 7.4`

`h = 7.4`

Answer 2

`color(purple)(h=7.4`

Explanation:

`-3/11=(5-h)/(h+1.4)`

`:.-3/11=(5-h)/(h+14/10)`

multiply L.H.S. and R.H.S. by `(h+14/10)`

`:.-3/11(h+14/10)=5-h`

`:.-3/11h-(14/10)(3/11)=5-h`

`:.-3/11h-42/110=5-h`

`:.-3/11h+h=5+42/110`

`:.-3/11h+11/11h=5+42/110`

`:.8/11h=5 42/110`

`:.8/11h=592/110`

:.`(80h=592)/110`

multiply L.H.S. and R.H.S. by `110`

`:.80h=592`

`:.h=592/80`

`:.color(purple)(h=7.4`

check:

substitute `color(purple)(h=7.4`

`:.-3/11=(5-7.4)/(7.4+1.4)`

`:.-3/11=-2.4/8.8`

`:.-3/11=-0.272727272`

`:.color(purple)(-0.272727272=-0.272727272`