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Which of the following equations have exactly one solution?
Choose all answers that apply:

12x + 12 = 13x + 12

-13x + 12 = 13x + 13

12x + 12 = 13x - 12

-13x+12=13x-13​

Respuesta :

calculista

Answer:

[tex]12x + 12 = 13x + 12[/tex]

[tex]-13x + 12 = 13x + 13[/tex]

[tex]12x + 12 = 13x - 12[/tex]

[tex]-13x+12=13x-13[/tex]

Step-by-step explanation:

Verify each case

case 1) we have

[tex]12x + 12 = 13x + 12[/tex]

Solve for x

Subtract 12x both sides

[tex]12 = 13x + 12-12x[/tex]

[tex]12 = x+ 12[/tex]

Subtract 12 both sides

[tex]12-12 = x[/tex]

Rewrite

[tex]x=0[/tex]

therefore

The equation has one solution

case 2) we have

[tex]-13x + 12 = 13x + 13[/tex]

Solve for x

Adds 13x both sides

[tex]12= 13x + 13+13x[/tex]

[tex]12= 26x + 13[/tex]

Subtract 13 both sides

[tex]12-13= 26x[/tex]

[tex]-1= 26x[/tex]

Divide by 26 both sides

[tex]x=-1/26[/tex]

therefore

The equation has one solution

case 3) we have

[tex]12x + 12 = 13x - 12[/tex]

Solve for x

Adds 12x both sides

[tex]12 = 13x - 12-12x[/tex]

[tex]12 = x- 12[/tex]

Adds 12 both sides

[tex]12+12 = x[/tex]

Rewrite

[tex]x=24[/tex]

therefore

The equation has one solution

case 4) we have

[tex]-13x+12=13x-13[/tex]

Solve for x

Adds 13x both sides

[tex]12=13x-13+13x[/tex]

[tex]12=26x-13[/tex]

Adds 13 both sides

[tex]12+13=26x[/tex]

[tex]25=26x[/tex]

Divide by 26 both sides and rewrite

[tex]x=25/26[/tex]

therefore

The equation has one solution

BasketballEinstein

Answer:

[tex]\displaystyle All\:of\:the\:above[/tex]

Explanation:

The swiftest way you can tell that all equations have one solution is that they each all have unique rate of changes [slopes].

I am joyous to assist you anytime.

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