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3 years ago

Tell whether each equation has one solution, infinitely many solutions, or no solution.

Mathematics

1 answer:

Phantasy [73]3 years ago

7 0

The equation 6x + 8 = 6(x + 2) has no solution

The equation 10x = 15 + 5x has one solution

The equation x + 11 = 8x + 11 - 7x has infinitely many solutions

Step-by-step explanation:

The types of the solutions of an equation of one variable

If the variable has one value, then the equation has one solution
If the variable disappears from the equation and the left hand side is equal to the right hand side, then the equation has infinitely many solutions
If the variable disappears from the equation and the left hand side is not equal the right hand side, then the equation has no solutions

∵ 6x + 8 = 6(x + 2)

- Simplify the right hand side

∴ 6x + 8 = 6x + 12

- Subtract 6 from both sides

∴ 8 = 12 ⇒ it can not be

- x disappears and the left hand side not equal the right and side,

then use the 3rd case above

∵ L.H.S ≠ R.H.S

∴ The equation has no solution

∵ 10x = 15 + 5x

- Subtract 5x from both sides

∴ 5x = 15

- Divide both sides by 5

∴ x = 3

- The variable x has one solution, then use the 1st case above

∴ The equation has one solution

∵ x + 11 = 8x + 11 - 7x

- Add the like terms in the right hand side

∴ x + 11 = x + 11

- Subtract x from both sides

∴ 11 = 11

- x disappears and the left hand side is equal to the right and side,

then use the 2nd case above

∵ L.H.S = R.H.S

∴ The equation has infinitely many solutions

Learn more:

You can learn more about the solutions of the equations in brainly.com/question/13168205

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