Answer: one solution x + 3 = 5 x = 2 no other other value for x is possible
No solution: (x + 3) = 2(x +3)
Infinitely many solutions: x+3 = 3 + x
Step-by-step explanation:
why (x + 3) = 2(x +3) has no solution. Can you solve?
x+3=2x+6 -x=3 x=-3 substute -3 for x
(-3)+ 3)= 2[(-3) +3]
-3+3 = -6 +3
0 = -3 False!
x+3 = 3 + x has infinitely many solutions. Substitute any number for x, and the equation is true (5)+3=3+(5) 8=8 . 11111+3 =3+11111 11114=11114
An equation can either have: one solution, no solution, or infinitely many solutions. Some equations that can be derived from [tex]x + 3[/tex] and their solution type are:
Given that:
[tex]Expression = x + 3[/tex]
Equation with one solution
For an equation to have one solution. then the equation is consistent and dependent.
For instance:
[tex]x + 3 = 2x[/tex]
Collect like terms to solve for x
[tex]2x -x = 3[/tex]
[tex]x =3[/tex]
This means that [tex]x =3[/tex] is the only solution to [tex]x + 3 = 2x[/tex].
Hence, [tex]x + 3 = 2x[/tex] has one solution
Equation with no solution
For an equation to have no solution. then both sides of the equation are not equal
For instance:
[tex]x + 3 = x[/tex]
Collect like terms to solve for x
[tex]x- x = 3[/tex]
[tex]0 = 3[/tex]
Because 0 is not equal to 3, then [tex]x + 3 = x[/tex] has no solution
Equation with infinitely many solutions
For an equation to have infinitely many solutions. then both sides of the equation must be the same thing
For instance:
[tex]x + 3 = 2(0.5x + 1.5)[/tex]
Open the bracket
[tex]x + 3 = x + 3[/tex]
Collect like terms
[tex]x - x = 3 - 3[/tex]
[tex]0 = 0[/tex]
Because both sides are the same (i.e. 0), then [tex]x + 3 = 2(0.5x + 1.5)[/tex] has infinitely many solutions
Read more about equation solutions at:
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