198k views
2 votes
Which of the following equations has the solution x = all real numbers?

Which of the following equations has the solution x = all real numbers?-example-1
User TiMoch
by
6.1k points

1 Answer

1 vote

Answer: 0 is a real number, and the only equation that gives us the solution of x to be zero are equation 1 and equation 4

The first equation is given as

4(3 - x) + 7x = 4x + 12 + 2x

Firstly, we need to open the parenthesis

4*3 - 4*x + 7x = 4x + 12 + 2x

12 - 4x + 7x = 4x + 12 + 2x

Collect the like terms

12 - 12 = 4x + 2x + 4x - 7x

0 = 10x - 7x

0 = 3x

Divide both sides by 3

0/3 = 3x/3

x = 0

For the second equation

3(4 - x) + 6x = 4x + 12 - x

Open the parenthesis

3*4 - 3*x + 6x = 4x + 12 - x

12 - 3x + 6x = 4x + 12 - x

Collect the like terms

12 - 12= 4x - x + 3x - 6x

0 = 6x - 6x

0 = 0......... No solution

Third equation

4(3 - x) + 6x = 3x + 8 - x

Open the parenthesis

4*3 - 4*x + 6x = 3x + 8 - x

Collect the like terms

12 - 4x + 6x = 3x + 8 - x

12 + 2x = 3x - x + 8

Collect the like terms

12 - 8 = 2x - 2x

4 = 0x

x = infinity

Fourth equation

4(4 - x) + 6x = x + 16 - 4x

Open the parenthesis

16 - 4x + 6x = x + 16 - 4x

16 + 2x = x - 4x + 16

16 - 16 = x - 4x - 2x

0 = -3x - 2x

0 = -5x

Divide both sides by -5

0/-5 = -5x / -5

x = 0

0 is a real number, and the only equation that gives us the solution of x to be zero are equation 1 and equation 4

User Jitty Aandyan
by
6.8k points