Question

Can someone please help me with number 37?

Answer 1

Answer:
`x=10`

Simplify both sides of the equation

`4-(3x-5)=6-(2x+7)`

`4+-1(3x-5)=6+-1(2x+7)` (Distribute the Negative Sign)

`4+-1(3x)+(-1)(-5)=6+-1(2x)+(-1)(7)`

`4+-3x+5=6+-2x+-7`

`(-3x)+(4+5)=(-2x)+(6+-7)` (Combine Like Terms)

`-3x+9=-2x+-1`

Add 2x to both sides

`-3x+9+2x=-2x-1+2x\\-x+9=-1`

Subtract 9 from both sides

`-x+9-9=-1-9\\-x=-10`

Divide both sides by -1

`-x/-1=-10/-1\\x=10`

Answer 2

x = 10

Explanation:

`4-(3x-5)=6-(2x+7)\\\\/-(a+b)=-1(a+b)=(-1)(a)+(-1)(b)-\text{distributive property}/\\\\4-3x-(-5)=6-2x-7\\\\4-3x+5=6-2x-7\qquad\text{combine like terms}\\\\-3x+(4+5)=-2x+(6-7)\\\\-3x+9=-2x-1\qquad\text{subtract 9 from both sides}\\\\-3x+9-9=-2x-1-9\\\\-3x=-2x-10\qquad\text{sdd}\ 2x\ \text{to both sides}\\\\-3x+2x=-2x+2x-10\\\\-x=-10\qquad\text{change the signs}\\\\\boxed{x=10}`