Algebra Practice Test

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Question: 1 / 400

How many solutions exist for the equations x - 2 = 5 and 2x + 3 = 15?

Zero

One

The equation \( x - 2 = 5 \) can be solved by isolating \( x \). Adding 2 to both sides gives:

\[

x = 5 + 2 = 7

\]

This means that there is one solution for the equation \( x - 2 = 5 \): \( x = 7 \).

Next, for the equation \( 2x + 3 = 15 \), we can isolate \( x \) by first subtracting 3 from both sides:

\[

2x = 15 - 3 = 12

\]

Now, dividing both sides by 2 results in:

\[

x = \frac{12}{2} = 6

\]

This indicates that there is also one solution for the equation \( 2x + 3 = 15 \): \( x = 6 \).

Since each equation yields a single, unique solution, the overall conclusion is that both equations have one solution each, but they do not intersect or yield the same solution. The question is asking about the total number of solutions across the two equations, and each equation is independently true for the value it provides.

Hence, the answer is that there is one solution

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