Question
The Usefulness of Graphs Quick Check
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Question
Use the image to answer the question.
Two lines slope upward on a coordinate plane. A solid line passes through the plotted point left parenthesis 2 comma 7 right parenthesis. A dotted line intersects the first line at the plotted point left parenthesis negative 1 comma 1 right parenthesis.
Use the function graphs to solve the equation 2x+3=3x+4
.
(1 point)
Responses
−1
negative 1
7
7
2
2
1
1
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Answers
GPT-4o mini
To solve the equation \( 2x + 3 = 3x + 4 \), we can simplify it step by step.
1. First, rearrange the equation to isolate \( x \):
\[
2x + 3 - 3 = 3x + 4 - 3
\]
This simplifies to:
\[
2x = 3x + 1
\]
2. Next, isolate \( x \) by subtracting \( 3x \) from both sides:
\[
2x - 3x = 1
\]
This simplifies to:
\[
-x = 1
\]
3. Finally, multiply both sides by -1 to solve for \( x \):
\[
x = -1
\]
Thus, the solution to the equation \( 2x + 3 = 3x + 4 \) is \( x = -1 \).
The correct response is:
- **−1**
1. First, rearrange the equation to isolate \( x \):
\[
2x + 3 - 3 = 3x + 4 - 3
\]
This simplifies to:
\[
2x = 3x + 1
\]
2. Next, isolate \( x \) by subtracting \( 3x \) from both sides:
\[
2x - 3x = 1
\]
This simplifies to:
\[
-x = 1
\]
3. Finally, multiply both sides by -1 to solve for \( x \):
\[
x = -1
\]
Thus, the solution to the equation \( 2x + 3 = 3x + 4 \) is \( x = -1 \).
The correct response is:
- **−1**