Question

Which of the equations shown have infinitely many solutions?
Select all that apply.
A. 3x – 1 = 3x + 1
B. 2x – 1 = 1 – 2x
C. 3x – 2 = 2x – 3
D. 3(x – 1) = 3x – 3
E. 2x + 2 = 2(x + 1)
F. 3(x – 2) = 2(x – 3)

Answer 1

Answer:

D. and E.

A. No solution

B. x = 1/2

C. x = -1

F. x = 0

Answer 2

Equations D and E will have infinitely many solutions.

An equation has a unique solution when there is a particular value of $x$ which satisfies the equation.

An equation has infinite solutions when the equation is true for every value of $x$.

An equation has no solution when the equation is not true for any value of $x$.

A. $3x-1=3x+1$

$-1=1$, there is not value of $x$ for which this is true.

So, this equation has no solution.

B. $2x-1=1-2x$

$2x+2x=1+1$

$4x=2$

$x=\frac{1}{2}$, this is a unique value.

So, the equation has a unique solution.

C. $3x-2=2x-3$

$x=-1$, this is a unique value.

So, the equation has a unique solution.

D. $3(x – 1) = 3x – 3$

$3x-3=3x-3$

$-3=-3$, which is always true.

So, the equation has infinitely many solutions.

E. $2x + 2 = 2(x + 1)$

$2x+2=2x+2$

$2=2$, which is always true.

So, the equation has infinitely many solutions.

F. $3(x - 2) = 2(x - 3)$

$3x-6=2x-6$

$x=0$, this is a unique value.

So, the equation has a unique solution.

So, equations D and E will have infinitely many solutions.

Learn more about solutions of an equation here:

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