3.
Which of the following equations has an infinite number of solutions? (1 point)
3x – 3 = –4x
2y + 4 – y = 16
7x + 5 = 4x + 5 + 3x
6y – 2 = 2(y – 1)
I think it's A.
7x + 5 = 4x + 5 + 3x
simplifies to
7x + 5 = 7x + 5
Which appears to then support any integer, so I think it's C.
to test:
7(*2) + 5 = 4(*2) + 5 + 3(*2)
14 + 5 = 8 + 5 + 6
19 = 19
to test:
7(*3) + 5 = 4(*3) + 5 + 3(*3)
21 + 5 = 12 + 5 + 9
26 = 26
and so on.
Nope. x = 3/7
There will be one where the variable just disappears, leaving a true equation. For example, if you have something like
2x-4 = x-4+x
that is true no matter what value you pick for x.
thank you guys! just in time.
To determine which equation has an infinite number of solutions, you need to solve each equation and check the solution sets.
Let's solve each equation step by step:
A: 3x - 3 = -4x
First, add 4x to both sides: 3x + 4x - 3 = 0
Combine like terms: 7x - 3 = 0
Then, add 3 to both sides: 7x - 3 + 3 = 0 + 3
Simplify: 7x = 3
Finally, divide both sides by 7: x = 3/7
B: 2y + 4 - y = 16
Combine like terms: y + 4 = 16
Then, subtract 4 from both sides: y + 4 - 4 = 16 - 4
Simplify: y = 12
C: 7x + 5 = 4x + 5 + 3x
Combine like terms: 7x = 7x + 5
Subtract 7x from both sides: 7x - 7x = 7x + 5 - 7x
Simplify: 0 = 5
This equation leads to a contradiction (0 = 5), meaning there are no solutions.
D: 6y - 2 = 2(y - 1)
First, distribute 2 on the right-hand side: 6y - 2 = 2y - 2
Then, add 2y to both sides: 6y - 2 + 2y = 2y - 2 + 2y
Simplify: 8y - 2 = 0
Finally, add 2 to both sides: 8y - 2 + 2 = 0 + 2
Simplify: 8y = 2
Divide both sides by 8: y = 2/8 or y = 1/4
Based on our solutions, equation C (7x + 5 = 4x + 5 + 3x) leads to a contradiction and has no solution, while equations A, B, and D have unique solutions.
Therefore, the equation that has an infinite number of solutions is not A but rather B (2y + 4 - y = 16), where y can take any value because it cancels out during the simplification process.