Question
Solve and Determine if the equation has one, none or infinite solutions.
-11 + x = -7x - 8(-x + 1)
-11 + x = -7x - 8(-x + 1)
Answers
GPT 3.5
To solve the equation, we will simplify both sides and combine like terms.
Starting with the left side of the equation:
-11 + x
And the right side of the equation:
-7x - 8(-x + 1)
Expanding the brackets on the right side:
-7x - 8(-x) - 8(1)
-7x + 8x - 8
Now combining like terms on the right side:
x - 8
The equation now becomes:
-11 + x = x - 8
To solve for x, we can start by moving all terms with x to one side of the equation and all constant terms to the other side.
Adding -x to both sides:
-11 = -8
We can see that we have a contradiction here (-11 does not equal -8), so this equation has no solutions.
Starting with the left side of the equation:
-11 + x
And the right side of the equation:
-7x - 8(-x + 1)
Expanding the brackets on the right side:
-7x - 8(-x) - 8(1)
-7x + 8x - 8
Now combining like terms on the right side:
x - 8
The equation now becomes:
-11 + x = x - 8
To solve for x, we can start by moving all terms with x to one side of the equation and all constant terms to the other side.
Adding -x to both sides:
-11 = -8
We can see that we have a contradiction here (-11 does not equal -8), so this equation has no solutions.
33 + 6x = 3(-1 + 5x)
GPT 3.5
To solve this equation, we will simplify both sides and combine like terms.
Starting with the left side of the equation:
33 + 6x
And the right side of the equation:
3(-1 + 5x)
Expanding the brackets on the right side:
3*(-1) + 3*5x
-3 + 15x
Now our equation becomes:
33 + 6x = -3 + 15x
To solve for x, we will again move all terms with x to one side and constant terms to the other side.
Subtracting 6x from both sides:
33 = -3 + 9x
Subtracting -3 from both sides:
33 + 3 = 9x
36 = 9x
Now, we can solve for x by dividing both sides by 9:
36/9 = x
4 = x
So, the equation has one solution, x = 4.
Starting with the left side of the equation:
33 + 6x
And the right side of the equation:
3(-1 + 5x)
Expanding the brackets on the right side:
3*(-1) + 3*5x
-3 + 15x
Now our equation becomes:
33 + 6x = -3 + 15x
To solve for x, we will again move all terms with x to one side and constant terms to the other side.
Subtracting 6x from both sides:
33 = -3 + 9x
Subtracting -3 from both sides:
33 + 3 = 9x
36 = 9x
Now, we can solve for x by dividing both sides by 9:
36/9 = x
4 = x
So, the equation has one solution, x = 4.
-5(x - 1) = 5 - 5x
GPT 3.5
To solve this equation, we will simplify both sides and combine like terms.
Starting with the left side of the equation:
-5(x - 1)
Expanding the bracket on the left side:
-5*x + (-5)(-1)
-5x + 5
And the right side of the equation:
5 - 5x
Now our equation becomes:
-5x + 5 = 5 - 5x
Next, we will move the x terms to one side and the constant terms to the other side.
Adding 5x to both sides:
-5x + 5 + 5x = 5 - 5x + 5x
Simplifying:
5 = 5
We can see that both sides of the equation are equal, meaning that the equation is true regardless of the value of x. Therefore, this equation has infinitely many solutions.
Starting with the left side of the equation:
-5(x - 1)
Expanding the bracket on the left side:
-5*x + (-5)(-1)
-5x + 5
And the right side of the equation:
5 - 5x
Now our equation becomes:
-5x + 5 = 5 - 5x
Next, we will move the x terms to one side and the constant terms to the other side.
Adding 5x to both sides:
-5x + 5 + 5x = 5 - 5x + 5x
Simplifying:
5 = 5
We can see that both sides of the equation are equal, meaning that the equation is true regardless of the value of x. Therefore, this equation has infinitely many solutions.
12 + 4n = 4(n + 3)
GPT 3.5
To solve this equation, we will simplify both sides and combine like terms.
Starting with the left side of the equation:
12 + 4n
And the right side of the equation:
4(n + 3)
Expanding the bracket on the right side:
4 * n + 4 * 3
4n + 12
Now our equation becomes:
12 + 4n = 4n + 12
We can see that both sides of the equation are equal. The equation is already simplified and has the same terms on both sides.
This means that the equation has infinitely many solutions, meaning that any value of n will satisfy the equation.
Starting with the left side of the equation:
12 + 4n
And the right side of the equation:
4(n + 3)
Expanding the bracket on the right side:
4 * n + 4 * 3
4n + 12
Now our equation becomes:
12 + 4n = 4n + 12
We can see that both sides of the equation are equal. The equation is already simplified and has the same terms on both sides.
This means that the equation has infinitely many solutions, meaning that any value of n will satisfy the equation.
4(-4 - 8m) + 28m + 4m = -272
GPT 3.5
To solve this equation, we will simplify both sides and combine like terms.
Starting with the left side of the equation:
4(-4 - 8m) + 28m + 4m
Expanding the first bracket:
4 * -4 + 4 * (-8m)
-16 - 32m
Now the left side of the equation becomes:
-16 - 32m + 28m + 4m
Combining like terms:
-16 - 32m + 32m
Now the left side of the equation becomes:
-16
Our equation now becomes:
-16 = -272
We can see that the equation is not true because -16 is not equal to -272.
Therefore, this equation has no solutions.
Starting with the left side of the equation:
4(-4 - 8m) + 28m + 4m
Expanding the first bracket:
4 * -4 + 4 * (-8m)
-16 - 32m
Now the left side of the equation becomes:
-16 - 32m + 28m + 4m
Combining like terms:
-16 - 32m + 32m
Now the left side of the equation becomes:
-16
Our equation now becomes:
-16 = -272
We can see that the equation is not true because -16 is not equal to -272.
Therefore, this equation has no solutions.