ecide whether each equation has one solution, no solutions, or infinitely many solutions.
1. 2(x – 3) = 2x (1 point)
one solution
no solutions
infinitely many solutions
2. 3(y – 3) = 2y – 9 + y (1 point)
one solution
no solutions
infinitely many solutions
3. 10x – 2 – 6x = 3x – 2 + x (1 point)
one solution
no solutions
infinitely many solutions
4. 4(x + 3) + 2x = x – 8 (1 point)
one solution
no solutions
infinitely many solutions
i mean
1b
2c
3c
4a
I think the answers are
1 c
2a
3b
4a
am i correcect steve
1. ok
2. ok
3. ok
4. ok
Good work!
thanks
To determine whether each equation has one solution, no solutions, or infinitely many solutions, we can solve each equation and analyze the solutions.
1. 2(x - 3) = 2x:
First, distribute the 2 on the left side:
2x - 6 = 2x
Next, subtract 2x from both sides to isolate the variable:
-6 = 0
Since -6 does not equal 0, we have a contradiction. Therefore, this equation has no solutions.
2. 3(y - 3) = 2y - 9 + y:
First, distribute the 3 on the left side:
3y - 9 = 2y - 9 + y
Next, combine like terms on both sides:
3y - 9 = 3y - 9
We can subtract 3y from both sides, which gives:
-9 = -9
Since -9 is equal to -9, this equation is true for all values of y. Therefore, this equation has infinitely many solutions.
3. 10x - 2 - 6x = 3x - 2 + x:
First, combine like terms on both sides:
4x - 2 = 4x - 2
We can subtract 4x from both sides, which gives:
-2 = -2
Since -2 is equal to -2, this equation is true for all values of x. Therefore, this equation has infinitely many solutions.
4. 4(x + 3) + 2x = x - 8:
First, distribute the 4 on the left side:
4x + 12 + 2x = x - 8
Next, combine like terms on both sides:
6x + 12 = x - 8
We can subtract x from both sides and subtract 12 from both sides to isolate the variable:
5x = -20
Finally, divide both sides by 5 to solve for x:
x = -4
Since x is equal to -4, this equation has one solution.
In summary:
1. This equation has no solutions.
2. This equation has infinitely many solutions.
3. This equation has infinitely many solutions.
4. This equation has one solution.