Solve each of the following equations algebraically and check the solution.
a 7+40=23
b
—2=4
3
12 = I)
c
a) 7 + 40 = 23
This equation is not true. There is no solution.
b) -2/3 = 4
To solve for the variable, we can multiply both sides of the equation by 3 to get rid of the denominator:
-2 = 4 * 3
Simplifying, we have:
-2 = 12
This equation is not true. There is no solution.
c) 12 = I
To solve for the variable, we want to isolate it on one side of the equation. In this case, the variable is already isolated. The solution is:
I = 12
To check the solution, substitute 12 back into the original equation:
12 = 12
This equation is true. The solution is correct.
For each of these equations, state the first operation you would apply to both sides to solve it.
2x+3=9`
b 4x-7=33
d 22 17)
C 5(a+3) 50
For the equation 2x + 3 = 9, the first operation to apply to both sides would be subtracting 3 from both sides. This will isolate the term with the variable on one side of the equation.
For the equation 4x - 7 = 33, the first operation to apply to both sides would be adding 7 to both sides to get rid of the negative constant term. This will isolate the term with the variable on one side of the equation.
For the equation 22 = 17, it is already solved. There is nothing to apply to both sides.
For the equation 5(a + 3) = 50, the first operation to apply to both sides would be dividing both sides by 5 to solve for the term within the parentheses.
a) 7 + 40 = 23
To solve this equation algebraically, we need to isolate the variable. Let's start by subtracting 7 from both sides of the equation:
7 + 40 - 7 = 23 - 7
40 = 16
Now we have reached a contradiction. 40 does not equal 16, so there is no solution to this equation.
b) -2/3 = 4
To solve this equation algebraically, we need to isolate the variable. Let's multiply both sides of the equation by 3:
3 * (-2/3) = 3 * 4
-2 = 12
Again, we have reached a contradiction. -2 does not equal 12, so there is no solution to this equation.
c) 12 = I
To solve this equation algebraically, we need to determine the value of I. Since I has no coefficient, we can consider it as a variable.
There is no equation given in the problem statement, so we do not have enough information to solve for I or check any solutions.