1# There are many solutions for the equation 2x - x + 7 = x + 3 + 4
2# There is no solution for the equation -2(x + 1) = -2x + 5
3# There is one solution for the equation 4x + 2x + 2 = 3x - 7
Step-by-step explanation:
The solution of an equation of one variable is
- One solution if the variable in the left hand side equal to a number in the right hand side
- No solution if the variable disappears and the left hand side not equal to the right hand side
- Many solutions if the variable disappears and the left hand side equal to the right hand side
1#
∵ 2x - x + 7 = x + 3 + 4
- Add the like terms in each side
∴ (2x - x) + 7 = x + (3 + 4)
∴ x + 7 = x + 7
- Subtract x from both sides
∴ 7 = 7
∵ Left hand side = right hand side
∴ x can be any number
∴ The equation has many solutions
There are many solutions for the equation 2x - x + 7 = x + 3 + 4
2#
∵ -2(x + 1) = -2x + 5
- Simplify the left hand side
∴ -2(x) + -2(1) = -2x + 5
∴ -2x - 2 = -2x + 5
- Add 2x for both sides
∴ -2 = 5
∵ Left hand side ≠ right hand side
∴ x can not be any value
∴ The equation has no solution
There is no solution for the equation -2(x + 1) = -2x + 5
3#
∵ 4x + 2x + 2 = 3x - 7
- Add the like terms in the left hand side
∴ (4x + 2x) + 2 = 3x - 7
∴ 6x + 2 = 3x - 7
- Subtract 3x from both sides
∴ 3x + 2 = -7
- Subtract 2 from both sides
∴ 3x = -9
- Divide both sides by 3
∴ x = -3
∵ x has a value
∴ The equation has one solution
There is one solution for the equation 4x + 2x + 2 = 3x - 7
Learn more:
You can learn more about the solutions of the equations in brainly.com/question/1626495
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