Question

How do you solve `T = (3/10)(Z - 12,000)` for Z?

Answer 1

`Z=10/3(T+3600)`

Explanation:

Given,

`T=3/10(Z-12000)`

Use the distributive property, `color(red)a(color(blue)b+color(purple)c)=color(red)acolor(blue)b+color(red)acolor(purple)c`, to expand the right side.

`T=3/10(Z)+3/10(-12000)`

`T=3/10Z+(3xx-12000)/10`

`T=3/10Z-36000/10`

`T=3/10Z-3600`

Isolate for `Z`. Start by adding `3600` to both sides.

`Tcolor(white)(i)color(red)(+3600)=3/10Z-3600color(white)(i)color(red)(+3600)`

`T+3600=3/10Z`

Divide both sides by `3/10`.

`color(red)((color(black)(T+3600))/(3/10))=color(red)((color(black)(3/10Z))/(3/10))`

`color(red)((color(black)(T+3600))/(3/10))=color(red)((color(black)(color(blue)cancelcolor(black)(3/10)Z))/(color(blue)cancelcolor(red)(3/10)))`

Note: Recall that dividing by a fraction is the same as multiplying by its reciprocal!

`Z=color(green)(|bar(ul(color(white)(a/a)color(black)(10/3(T+3600))color(white)(a/a)|)))`