Solving Linear Equations Online Practice

Question

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Question
Which of the following equations has exactly one solution?(1 point)
Responses

5x+4=5x+4
5 x plus 4 equals 5 x plus 4

5x+4=5x+3
5 x plus 4 equals 5 x plus 3

−5x+4=5x+4
negative 5 x plus 4 equals 5 x plus 4

−5x+3=−5x+3

Answer 1

To determine which equation has exactly one solution, let's analyze each option:

1. 5x + 4 = 5x + 4

   • This simplifies to the same expression on both sides, which means there are infinitely many solutions (any value of x will satisfy the equation).

2. 5x + 4 = 5x + 3

   • If we try to solve this, we can subtract \(5x\) from both sides: \(4 = 3\), which is not true. Hence, this equation has no solution.

3. −5x + 4 = 5x + 4

   • If we solve this equation, we can first add \(5x\) to both sides: \(4 = 10x + 4\). Subtracting \(4\) from both sides gives: \(0 = 10x\). Dividing by \(10\): \(x = 0\), which means there is exactly one solution.

4. −5x + 3 = −5x + 3

   • Similar to the first equation, this simplifies to the same expression on both sides, leading to infinitely many solutions.

Based on this analysis, the equation that has exactly one solution is:

−5x + 4 = 5x + 4.