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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