Equations:
[tex]x+6=5+x[/tex]
[tex]-2(x-3)=-2x+6[/tex]
[tex]4-4x=3x+2[/tex]
[tex]4(x+1)=3(x+2)[/tex]
[tex]5-3x=-3x+4[/tex]
Answer:
[tex]x+6=5+x[/tex]
[tex]5-3x=-3x+4[/tex]
Step-by-step explanation:
Given
[tex]x+6=5+x[/tex]
[tex]-2(x-3)=-2x+6[/tex]
[tex]4-4x=3x+2[/tex]
[tex]4(x+1)=3(x+2)[/tex]
[tex]5-3x=-3x+4[/tex]
Required:
Which have no solution
[tex]x+6=5+x[/tex]
Subtract x from both sides
[tex]x -x+6 = 5 + x - x[/tex]
[tex]6 = 5[/tex]
[tex]x+6=5+x[/tex] has no solution because [tex]6 \ne 5[/tex]
[tex]-2(x-3)=-2x+6[/tex]
Open bracket
[tex]-2x + 6 = -2x + 6[/tex]
Both sides are equal.
Hence, there is an [tex]Infinite\ Number[/tex] of Solutions
[tex]4-4x=3x+2[/tex]
Collect like terms
[tex]-3x - 4x = 2 - 4[/tex]
[tex]-7x = -2[/tex]
Solve for x
[tex]x = \frac{-2}{-7}[/tex]
[tex]x = \frac{2}{7}[/tex] --- This has a solution
[tex]4(x+1)=3(x+2)[/tex]
Open brackets
[tex]4x + 4 = 3x + 6[/tex]
Collect like terms
[tex]4x-3x = 6 - 4[/tex]
[tex]x = 2[/tex] --- This has a solution
[tex]5-3x=-3x+4[/tex]
Add 3x to both sides
[tex]5 - 3x + 3x = -3x + 3x + 4[/tex]
[tex]5 = 4[/tex]
[tex]5-3x=-3x+4[/tex] has no solution because [tex]5 \ne 4[/tex]
