Answer :
Equations with same terms on both sides, like "-76x + 76 = -76x + 76" & "76x + 76 = 76x + 76," have infinitely many solutions.
The equations with infinitely many solutions, [tex]\(-76x + 76 = -76x + 76\) and \(76x + 76 = 76x + 76\)[/tex], are considered identities. An identity is an equation that holds true for all values of the variable involved. In these equations, both sides are identical, which means no matter what value [tex]\(x\)[/tex] takes, both sides will always be equal.
For instance, in the equation [tex]\(-76x + 76 = -76x + 76\)[/tex], subtracting [tex]\(-76x\)[/tex] from both sides results in [tex]\(76 = 76\)[/tex], which is always true. Similarly, in the equation [tex]\(76x + 76 = 76x + 76\)[/tex], subtracting [tex]\(76x\)[/tex] from both sides yields [tex]\(76 = 76\)[/tex], again always true.
The reason these equations have infinitely many solutions is that they essentially state that the same value is equal to itself, regardless of the value of [tex]\(x\)[/tex]. This property makes them true for all possible values of [tex]\(x\),[/tex] hence they have an infinite number of solutions.
While the other equations provided, [tex]\(76x + 76 = -76x + 76\) and \(-76x + 76 = 76x + 76\)[/tex], do have solutions, they don't have infinitely many solutions because they represent specific relationships between the variables that are not universally true for all values of [tex]\(x\).[/tex]
The complete question is :
Which of the following equations have infinitely many solutions? Choose all answers that apply: -76x+76=-76x+76 76x+76=-76x+76 76x+76=76x+76 -76x+76=76x+76 .
