Aanya wrote the four equations that are shown below. she examined them, without solving them, to determine which has exactly one solution. which of aanya's equations has exactly one solution a: 6x-8=4(x-2)+2x b: 3(x-1)+2x=3(x-1)+2 c: 7x+2-x=6(x+2) d: 4(x+3)+x=5(x+1)+7

B:3(x-1)+2x=3(x-1)+2

Step-by-step explanation:

Aanya wrote the four equations that are shown below.

We need to check each equation and see which equations have same coefficient of x terms on both sides of equation.

A: 6x-8=4(x-2)+2x

Distribute 4 inside the parenthesis

6x-8=4x- 8+2x

We know 4x + 2x is 6x. So, both sides we have 6x. Hence no solution for this equation.

B:3(x-1)+2x=3(x-1)+2

Distribute 3 inside the parenthesis

3x - 3 + 2x = 3x - 3 + 2

5x - 3 = 3x- 3 + 2

Coefficient of x  are not same on both sides. So this equation has exactly one solution.

C:7x+2-x=6(x+2)

Distribute 6 inside the parenthesis

6x + 2= 6x + 12

Both sides we have 6x. Hence no solution for this equation.

D:4(x+3)+x=5(x+1)+7

Distribute 4  and 5 inside the parenthesis

5x + 12= 5x  + 5+ 12

Both sides we have 5x. Hence no solution for this equation.

The actual answer is C.

Hope I helped, it’s right on Ed genuity

Step-by-step explanation:

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step-by-step explanation:

d, x=8

step-by-step explanation:

simplifying

4x + -5 = 2x + 11

reorder the terms:

-5 + 4x = 2x + 11

reorder the terms:

-5 + 4x = 11 + 2x

solving

-5 + 4x = 11 + 2x

solving for variable 'x'.

move all terms containing x to the left, all other terms to the right.

add '-2x' to each side of the equation.

-5 + 4x + -2x = 11 + 2x + -2x

combine like terms: 4x + -2x = 2x

-5 + 2x = 11 + 2x + -2x

combine like terms: 2x + -2x = 0

-5 + 2x = 11 + 0

-5 + 2x = 11

add '5' to each side of the equation.

-5 + 5 + 2x = 11 + 5

combine like terms: -5 + 5 = 0

0 + 2x = 11 + 5

2x = 11 + 5

combine like terms: 11 + 5 = 16

2x = 16

divide each side by '2'.