Question
Determine how many solutions each equation has.
3 (x + 3) = 7 + 3x + 6 - x
8 (x + 2) = 5x + 16 + 3x
6x + 2 - 4x = 2 (x + 2)
3 (x + 3) = 7 + 3x + 6 - x
8 (x + 2) = 5x + 16 + 3x
6x + 2 - 4x = 2 (x + 2)
Answers
Answered by
GPT 3.5
To determine the number of solutions for each equation, simplify and solve for x:
1) 3 (x + 3) = 7 + 3x + 6 - x
Simplify: 3x + 9 = 13 + 2x
Combine like terms: x = 4
The equation has one solution.
2) 8 (x + 2) = 5x + 16 + 3x
Simplify: 8x + 16 = 8x + 16
The equation is an identity. It is true for all values of x.
The equation has infinitely many solutions.
3) 6x + 2 - 4x = 2 (x + 2)
Simplify: 2x + 2 = 2x + 4
Subtract 2x from both sides: 2 = 4
The equation has no solution.
1) 3 (x + 3) = 7 + 3x + 6 - x
Simplify: 3x + 9 = 13 + 2x
Combine like terms: x = 4
The equation has one solution.
2) 8 (x + 2) = 5x + 16 + 3x
Simplify: 8x + 16 = 8x + 16
The equation is an identity. It is true for all values of x.
The equation has infinitely many solutions.
3) 6x + 2 - 4x = 2 (x + 2)
Simplify: 2x + 2 = 2x + 4
Subtract 2x from both sides: 2 = 4
The equation has no solution.