Question

How do you solve `4(x+3)=5(x-2)`?

Answer 1

`x=22`

Explanation:

`color(blue)(4(x+3)=5(x-2)`

Use distributive property `color(green)(a(b+c)=ab+ac`

`rarr4x+12=5x-10`

Add `10` to both sides

`rarr4x+12+10=5x-10+10`

`rarr4x+22=5x`

Subtract `4x` both sides

`rarr4x+22-4x=5x-4x`

`rarr22=x`

Check

`color(brown)(4(22+3)=5(22-2)`

`color(brown)(4(25)=5(20)`

`color(brown)(100=100`

It's correct!!! =)

Answer 2

`x=22`

Explanation:

We can use the distributive property to simplify the left and right sides respectively to get

`4x+12=5x-10`

Next, we can add `10` to both sides to get

`4x+22=5x`, which is the same as

`5x=4x+22`

Lastly, we can subtract `4x` from both sides to get

`x=22`

Hope this helps!