Answer:
Part 1) The numbers are 22,24 and 26
Part 2) The value of x has no solution
Part 3) The value of x has no solution
Part 4) The value of x is [tex]x=-3.5[/tex]
Step-by-step explanation:
Part 1)
Let
x ----> the first even number
x+2 ---> the second consecutive even number
x+4 ---> the third consecutive even number
we know that
[tex]2(x)=(x+2)+20[/tex]
Solve for x
[tex]2x=x+22[/tex]
[tex]2x-x=22[/tex]
[tex]x=22[/tex]
therefore
The numbers are 22,24 and 26
Part 2) we have
[tex]10x-5-2(x+7)=2(4-x)+10x[/tex]
Distribute in the left and the right side to remove the parenthesis
[tex]10x-5-2x-14=8-2x+10x[/tex]
Combine like terms
[tex]8x-19=8x+8[/tex]
[tex]-19=8[/tex] -----> is not true
therefore
The value of x has no solution
Part 3) we have
[tex]-4x+5-1(x-4)=5x+5+4(1-3x)[/tex]
Distribute in the left and the right side to remove the parenthesis
[tex]-4x+5-x+4=5x+5+4-12x[/tex]
Combine like terms
[tex]-5x+9=-7x+9[/tex]
[tex]-5x=-7x[/tex] -----> is not true
therefore
The value of x has no solution
Part 3) we have
[tex]8-(9x+6)=5x+5+4(1-3x)[/tex]
Distribute in the right side to remove the parenthesis
[tex]8-9x-6=5x+5+4-12x[/tex]
Combine like terms
[tex]2-9x=-7x+9[/tex]
[tex]9x-7x=2-9[/tex]
[tex]2x=-7[/tex]
[tex]x=-3.5[/tex]
