Question

1. How many solitions does this equation have -4(5-3x)=12x+20

2. How many solutions does this equation have 3x+7(x+1)=2(6x+5)-2

Answer 1

1. no solutions

2. one solution

Explanation:

1. -4(5-3x)=12x+20

-20+12x=12x+20

-40+12x=12x

-40=0?????

So no solutions.

2. 3x+7(x+1)=2(6x+5)+2

3x+7x+7=12x+10+2

10x+7=12x+12

-2x+7=12

-2x=5

x=-5/2

So one solution.

Answer 2

The answers are:

1. No solution.

2. One solution:
`x=-(1)/(2)`

Explanation:

In order to determine the solutions for both equations, we have to solve every one. In any equation of one variable, we could get three types of solution:

1. One solution. The variable has a unique value.
2. No solution. The equality is not fulfilled.
3. Infinite solution. The variable is eliminated from the equation and the equality is fulfilled.

So, solving both equation:

1.-

`-4(5-3x)=12x+20\\-20+12x=12x+20\\12x-12x=20+20\\0=40\\`

The equality is not fulfilled. There is not solution.

2.-

`3x+7(x+1)=2(6x+5)-2\\3x+7x+7=12x+10-2\\10x-12x=8-7\\-2x=1\\x=-(1)/(2)`

There is one solution.
`x=-(1)/(2)`

Finally, the answers for both questions are:

1. No solution.

2. One solution:
`x=-(1)/(2)`