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

Feb 21, 2016

$x = 22$

#### Explanation:

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

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

$\rightarrow 4 x + 12 = 5 x - 10$

Add $10$ to both sides

$\rightarrow 4 x + 12 + 10 = 5 x - 10 + 10$

$\rightarrow 4 x + 22 = 5 x$

Subtract $4 x$ both sides

$\rightarrow 4 x + 22 - 4 x = 5 x - 4 x$

$\rightarrow 22 = x$

Check

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

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

color(brown)(100=100

It's correct!!! =)

Aug 4, 2018

$x = 22$

#### Explanation:

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

$4 x + 12 = 5 x - 10$

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

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

$5 x = 4 x + 22$

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

$x = 22$

Hope this helps!