Answer:
5/c * x + 7 = 22 (given)
5/c * x = 15 (subtraction property of equality)
5x = 15c (distributive property)
x = 3c (division property of equality)
Explanation:
Given: 5/c * x + 7 = 22
To prove: x = 3c
Step 1: Using the subtraction property of equality, we can subtract 7 from both sides of the equation to isolate the term involving x:
5/c * x + 7 - 7 = 22 - 7
This simplifies to:
5/c * x = 15
Step 2: To get x alone on one side of the equation, we can use the multiplication property of equality. We can multiply both sides of the equation by the reciprocal of 5/c, which is c/5:
(5/c * x) * (c/5) = 15 * (c/5)
On the left side, the c and 5 will cancel out, leaving us with:
x = 3c
Now, we have successfully proven that x = 3c using the given equation and properties of equality. The correct matches are:
1. addition property of equality - Not used in this proof.
2. division property of equality - x = 3c
3. given - 5/c * x + 7 = 22
4. distributive property - Not used in this proof.
5. multiplication property of equality - (5/c * x) * (c/5) = 15 * (c/5)
6. subtraction property of equality - 5/c * x + 7 - 7 = 22 - 7