3. Which of the following equations has an infinite number of solutions?
3x – 3 = –4x
2y + 4 – y = 16
7x + 5 = 4x + 5 + 3x
6y – 2 = 2(y – 1)
7x + 5 = 4x + 5 + 3x
is
7 x + 5 = 7 x + 5
that works for any old x
so its c
Come on Jman - Follow my directions and answer the question for yourself.
LOL, well try an infinite number of values for x in the third equation ! They all work.
so it is! right?
To determine which equation has an infinite number of solutions, we need to look for an equation where both sides are equal regardless of the value of the variable.
Let's go through each equation one by one:
1) 3x – 3 = –4x
To solve this equation, we need to isolate the variable x. First, we can combine like terms by adding 4x to both sides:
3x + 4x – 3 = 0
This simplifies to:
7x – 3 = 0
Next, we can move the constant term -3 to the other side by adding 3 to both sides:
7x = 3
Finally, we divide both sides of the equation by 7 to solve for x:
x = 3/7
As a result, this equation has only one solution, x = 3/7.
2) 2y + 4 – y = 16
To solve this equation, we combine like terms by subtracting y from 2y:
y + 4 = 16
Next, we can move the constant term 4 to the other side by subtracting 4 from both sides:
y = 16 -4
This simplifies to:
y = 12
Therefore, this equation has a single solution, y = 12.
3) 7x + 5 = 4x + 5 + 3x
To solve this equation, we can simplify both sides by combining like terms:
7x + 5 = 7x + 5
Here, you can see that both sides of the equation are identical, meaning that no matter what value x takes, the equation will always be true. Therefore, this equation has an infinite number of solutions.
4) 6y – 2 = 2(y – 1)
To solve this equation, we can distribute 2 on the right side of the equation:
6y – 2 = 2y – 2
Next, we can combine like terms by subtracting 2y from both sides:
4y – 2 = –2
To isolate the variable y, we add 2 to both sides:
4y = 0
Finally, we divide both sides by 4 to solve for y:
y = 0
Hence, this equation has a single solution, y = 0.
Therefore, the equation that has an infinite number of solutions is 7x + 5 = 4x + 5 + 3x.