Match the equation with the number of solutions for x that are possible.
Column A
1.
:
2.
y+5=12
:
y+5=12
3.
6a+1=9a:
6a+1=9a
4.
5x - 9 = 5x + 5:
5x - 9 = 5x + 5
5.
4(x - 7) +3x = 7x -28:
4(x - 7) +3x = 7x -28
Column B
a.Infinite solutions
b.One solution
c.No solution
d.Three solutions
e.There is no way to know
f.Two solutions
1. c. No solution
2. b. One solution
3. a. Infinite solutions
4. e. There is no way to know
5. f. Two solutions
Let's go through each equation in column A and determine the number of solutions for x that are possible.
1. y + 5 = 12: This equation represents a simple linear equation. By subtracting 5 from both sides, we get y = 7. Since there is no x term in the equation, it means x can take any value. Therefore, this equation has infinite solutions. The matching answer in column B would be a. Infinite solutions.
2. y + 5 = 12: This is the same equation as in equation 1. Hence, it has the same solution. Therefore, for this equation as well, the matching answer in column B is a. Infinite solutions.
3. 6a + 1 = 9a: This equation is also a linear equation, but it involves the variable a instead of x. To find the solution for a, we can subtract 6a from both sides, which gives us 1 = 3a. Then, divide both sides by 3 to solve for a, and we get a = 1/3. Since there is one unique solution for a, the matching answer in column B is b. One solution.
4. 5x - 9 = 5x + 5: This equation contains the variable x but leads to a contradiction. Subtracting 5x from both sides gives us -9 = 5, which is not true. This implies that there are no possible solutions for x in this equation. The matching answer in column B is c. No solution.
5. 4(x - 7) + 3x = 7x - 28: To solve this equation, we can start by simplifying the expression on the left side. Distributing 4 to (x - 7) gives us 4x - 28, so our equation becomes 4x - 28 + 3x = 7x - 28. Combining like terms, we have 7x - 28 = 7x - 28. Here, the variable x cancels out on both sides, leaving us with a true statement -28 = -28. This means the equation holds true for all values of x. So, similar to equation 1 and 2, this equation also has infinite solutions. The matching answer in column B is a. Infinite solutions.
To summarize, the matching answers for column A equations in column B are:
1. a. Infinite solutions
2. a. Infinite solutions
3. b. One solution
4. c. No solution
5. a. Infinite solutions
Let's go through each equation in Column A and determine the number of solutions for x.
1. y + 5 = 12:
This is a linear equation in one variable. By simplifying it, we get y = 7. Since there is no mention of x in the equation, there are infinite solutions for x. So, the answer for equation 1 in Column B is a. Infinite solutions.
2. y + 5 = 12:
This is the same equation as the first one. As mentioned earlier, there are infinite solutions for x. So, the answer for equation 2 in Column B is also a. Infinite solutions.
3. 6a + 1 = 9a:
This is a linear equation in one variable. By simplifying it, we get 1 = 3a. Solving for a, we find a = 1/3. So, there is only one solution for x. The answer for equation 3 in Column B is b. One solution.
4. 5x - 9 = 5x + 5:
This equation simplifies to -9 = 5. As -9 is not equal to 5, there is no solution for x. The answer for equation 4 in Column B is c. No solution.
5. 4(x - 7) + 3x = 7x - 28:
Expanding and simplifying this equation, we get 4x - 28 + 3x = 7x - 28, which further simplifies to 7x - 28 = 7x - 28. Here, the left-hand side is equal to the right-hand side, indicating that both sides are equal for all values of x. Therefore, there are infinite solutions for x. The answer for equation 5 in Column B is a. Infinite solutions.
To summarize:
Equation 1: a. Infinite solutions
Equation 2: a. Infinite solutions
Equation 3: b. One solution
Equation 4: c. No solution
Equation 5: a. Infinite solutions