Tim is working to determine if each equation given by his teacher has zero, one or infinite solutions. You need to identify his mistake for each problem, work out the correct solution and submit the work on #3. Click Here for Rubric
On the next question you will be required to show your work for this problem.
Question A.
9(5x+4)+5+x=45x+40
First we will "Distribute the 9 first."
9⋅5x+9⋅4+5+x=45x+40
Next we will simplify.
45x+36+5+x=45x+40
Now we will combine like terms.
45x+41=45x+40
Subtract
41=40
So this means there are zero solutions.
The correct answer is: (if there are infinite solutions then type "infinite" otherwise state the value for
x.
x=
The mistake in Tim's work is in the simplification step. Here is the correct solution:
9(5x+4)+5+x = 45x+40
Distribute the 9:
45x+36+5+x = 45x+40
Combine like terms:
46x+41 = 45x+40
Subtract 45x from both sides:
x+41 = 40
Subtract 41 from both sides:
x = -1
So the correct solution is x = -1.
The mistake made by Tim in this problem is in the step where he combines like terms.
The correct solution would be:
Simplifying the left side of the equation:
45x + 36 + 5 + x = 45x + 40
Combining like terms:
46x + 41 = 45x + 40
Subtracting 45x from both sides:
x + 41 = 40
Subtracting 41 from both sides:
x = -1
So the correct value for x is -1.
To identify Tim's mistake, we can look at the step where he combined like terms. He incorrectly simplified the equation by adding x to both sides, which led to an incorrect result.
To find the correct solution, let's go through the steps again.
Starting with the equation: 9(5x+4)+5+x=45x+40
First, we distribute the 9 to the terms inside the parentheses:
45x + 36 + 5 + x = 45x + 40
Next, we combine like terms:
46x + 41 = 45x + 40
Now, to solve for x, we want to isolate x on one side of the equation. To do this, we can subtract 45x from both sides:
46x - 45x + 41 = 45x - 45x + 40
This simplifies to:
x + 41 = 40
Finally, we subtract 41 from both sides to solve for x:
x + 41 - 41 = 40 - 41
x = -1
Therefore, the correct solution for x is -1.