Question

Use the drop down menus to complete each equation so the statement about its solution is true.

No solutions:
6-3+4x+1= __x + __

One solution:
6-3+4x+1= __x + __

Infinitely many solutions:
6-3+4x+1 = __x + __

Can someone explain to me how to find the answer for the blanks because I've tried many times to solve it and I keep getting it wrong :/

Answer 1

Explanation:

6 - 3 + 4x + 1

simplify this and you get: 4x + 4

If there are no solutions, then the equation will be equal to 4x + (any number other than 4). This will result in parallel lines.

Examples: 4x + 1, 4x + 2, 4x + 3

If there is one solution, then the equation will be equal to (any number other than 4)x + (any number). This will result in two lines that cross.

Examples: 3x + 1, 2x + 3, x + 4

If there are infinitely many solutions, then the equation will be equal to 4x + 4. This will result in both equations being the same line.

Examples: 4x + 4, 8x + 8, 2x + 2

Answer 2

When we solve a one variable equation, then two cases are possible,

(i) Variable can not remove from the equation,

In this condition the equation has only one solution,

(ii) Variable can remove from the equation,

There are further two cases,

(a) No solution : If after solving, we get a wrong statement,

(b) Infinitely many solutions : If after solving, we get a true statement,

Thus, by the above explanation,

We can say,

No solutions:

if 6 - 3 + 4x + 1 = 4x + 1 ( ∵ 3 ≠ 0 )

One solution:

6 - 3 + 4x + 1 = 3x + 1

(Note : put any number other than 4 as the coefficient of x in right side).

Infinitely many solutions:

6 - 3 + 4x + 1 = 4x + 4 ( ∵ 6 - 3 + 1 = 4 )