Question

1. circle the name of the student who correctly wrote the equation modeled below. then, find the solution to the equation.

penny: 2x=-8 - x
finley: 2 = 8 + x
gene: 2=-8 - x
asia: 2x=-6x - 1
solution: - 10

1. write and solve the equation modeled below.

equation:
solution: x=

Explanation:

Step1: Analyze the first balance problem

On the left - hand side of the first balance, we have \(2\) unit positive blocks, and on the right - hand side, we have \(8\) unit negative blocks and \(1\) negative \(x\) block. So the equation is \(2=-8 - x\), which means Gene wrote the correct equation.

Step2: Solve the equation \(2=-8 - x\)

Add \(8\) to both sides of the equation. \(2 + 8=-8 - x+8\), which simplifies to \(10=-x\). Multiply both sides by \(- 1\) to get \(x=-10\).

Step3: Analyze the second balance problem

On the left - hand side of the second balance, we have \(3\) \(x\) blocks and \(1\) negative unit block (\(3x - 1\)), and on the right - hand side, we have \(4\) unit positive blocks. So the equation is \(3x-1 = 4\).

Step4: Solve the equation \(3x-1 = 4\)

Add \(1\) to both sides: \(3x-1 + 1=4 + 1\), which gives \(3x=5\). Then divide both sides by \(3\): \(x=\frac{5}{3}\).

Answer:

1. The student who correctly wrote the equation is Gene, and the solution of the equation \(2=-8 - x\) is \(x = - 10\).
2. Equation: \(3x-1 = 4\), Solution: \(x=\frac{5}{3}\)