The Usefulness of Graphs Quick Check

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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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Answer 1

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