Which of the following equations has an infinite number of solutions?
a. 3x – 3 = –4x
b. 2y + 4 – y = 16
c. 7x + 5 = 4x + 5 + 3x
d. 6y – 2 = 2(y – 1)
And please explain how I don't understand. Thanks sooooo much!!!
look at c. Why can't you solve for x, as in the others?
The reason the that C has an infinite number of solutions as opposed to the others is because you essentially have
7x +5 = 7x +5 (because you can add the
4x and 3x to make 7x so any answer will work because it will be the same answer on each side no matter what and the other problems will all end up with X = to something were as C would end up 0=0
a.
3 x – 3 = – 4 x Add 4x to both sides
3 x – 3 + 4 x = – 4 x 4 x
7 x - 3 = 0 Add 3 to bozh sides
7 x - 3 + 3 = 0 + 3
7 x = 3 Divide both sides by 7
x = 3 / 7
ONLY ONE SOLUTION
b.
2 y + 4 – y = 16
y + 4 = 16 Subtracr 4 to both sides
y + 4 - 4 = 16 - 4
y = 12
ONLY ONE SOLUTION
c.
7 x + 5 = 4 x + 5 + 3 x
7 x + 5 = 7 x + 5
THAT IS TRUE FOR ALL VALUES OF x.
INFINITE NUMBER OF SOLUTIONS
d.
6 y – 2 = 2 ( y – 1 ) Divide both sides by 2
3 y - 1 = y - 1 Subtract y to both sides
3 y - y - 1 = - y - 1 - y
2 y - 1 = - 1 Add 1 to both sides
2 y - 1 + 1 = - 1 + 1
2 y = 0 Divide both sides by 2
y = 0
ONLY ONE SOLUTION
CORRECT ANSWER :
c
To determine which equation has an infinite number of solutions, we need to observe the equations closely and see if any variables can be eliminated or simplified in a way that would result in two equal constants.
Let's analyze each of the given options:
a. 3x – 3 = –4x
To solve this equation, we can start by combining like terms. Adding 4x to both sides:
3x + 4x – 3 = 0
Simplifying:
7x – 3 = 0
We can solve this equation by adding 3 to both sides:
7x = 3
Finally, dividing both sides by 7, we get:
x = 3/7
Since x represents a single value, there is only one solution to this equation.
b. 2y + 4 – y = 16
To solve this equation, we can combine like terms. Subtracting y from both sides:
2y – y + 4 = 16
Simplifying further:
y + 4 = 16
Now, we can isolate the variable by subtracting 4 from both sides:
y = 16 – 4
y = 12
Similar to the previous case, this equation also has only one solution.
c. 7x + 5 = 4x + 5 + 3x
To solve this equation, we can combine like terms. Adding 4x and 3x on the right side:
7x + 5 = 7x + 5
Notice that the equation simplifies to 7x + 5 = 7x + 5. In this case, both sides of the equation are identical, meaning the equation is true for all values of x. Therefore, there are an infinite number of solutions for this equation.
d. 6y – 2 = 2(y – 1)
To solve this equation, we can start by simplifying the right side using the distributive property:
6y – 2 = 2y – 2
Next, we can subtract 2y from both sides:
6y – 2y – 2 = -2
Now, let's simplify further:
4y – 2 = -2
To isolate the variable, let's add 2 to both sides:
4y = 0
Finally, dividing both sides by 4, we obtain:
y = 0
Similar to the previous cases, this equation also has a single solution.
Among the given options, only equation c, 7x + 5 = 4x + 5 + 3x, has an infinite number of solutions.