Question

How do you solve `2(4z-1)=3(z+2)`?

Answer 1

`z=8/5`

Explanation:

First, distribute the 2 and the 3 on their respective sides:

`8z-2=3z+6`

Then add 2 to both sides to begin isolating the z:

`8z=3z+8`

Then subtract 3z from both sides:

`5z=8`

Which then gives you your answer:

`z=8/5 or 1.6`

Answer 2

`z=8/5`, `1 3/5`, or `1.6`.

Explanation:

Solve:

`2(4z-1)=3(z+2)`

Expand.

`8z-2=3z+6`

Subtract `3z` from both sides.

`8z-3z-2=color(red)cancel(color(black)(3z))+6-color(red)cancel(color(black)(3z))`

Simplify.

`5z-2=6`

Add `2` to both sides.

`5z-color(red)cancel(color(black)(2))+color(red)cancel(color(black)(2))=6+2`

Simplify.

`5z=8`

Divide both sides by `5`.

`(color(red)cancel(color(black)(5))^1z)/color(red)cancel(color(black)(5))^1=8/5`

`z=8/5`

We can convert the improper fraction `8/5` to a mixed number, `color(red)(a) color(blue)(b)/color(green)(c)`. Divide the numerator by the denominator by long division to get a whole-number quotient and a remainder.

`8-:color(green)(5)= color(red)(1), "remainder" color(blue)(3)`

The whole number `color(red)1` is the whole number of the mixed number, the remainder `color(blue)3` is the numerator, and the divisor is the denominator `color(green)5`.

`8/5=color(red)(1) color(blue)(3)/color(green)(5`

The decimal number is `8-:5=1.6`