Mathematics, 13.10.2020 19:01 iluvdolantwins

sing the expression x + 3, write one equation that has one solution, one equation that has no solution, and one equation that has infinitely many solutions. Explain

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Answer from: jsph5332

An equation can either have: one solution, no solution, or infinitely many solutions. Some equations that can be derived from x + 3 and their solution type are:

has one solution x + 3 = x

has no solution x + 3 = 2(0.5x + 1.5)

has one solution

Given that:

Expression = x + 3

Equation with one solution

For an equation to have one solution. then the equation is consistent and dependent.

For instance:

x + 3 = 2x

Collect like terms to solve for x

2x -x = 3

x =3

This means that x =3 is the only solution to x + 3 = 2x .

Hence, x + 3 = 2x 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:

x + 3 = x

Collect like terms to solve for x

x- x = 3

0 = 3

Because 0 is not equal to 3, then x + 3 = x 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:

x + 3 = 2(0.5x + 1.5)

Open the bracket

x + 3 = x + 3

Collect like terms

x - x = 3 - 3

0 = 0

Because both sides are the same (i.e. 0), then x + 3 = 2(0.5x + 1.5) has infinitely many solutions

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