Question

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

benny
$2x = -8 - x$
finley
$2 = 8 + x$
gene
$2 = -8 - x$
asia
$2x = -6x - 1$
solution:

1. write and solve the equation modeled below.

equation:
solution:

Explanation:

Question 11

Step1: Analyze the balance model

On the left side of the balance, we have two \(1\) blocks, so that's \(1 + 1 = 2\). On the right side, we have one \(-x\) block and eight \(-1\) blocks, so that's \(-x + (-1)\times8=-x - 8\). Since the balance is equal, the equation is \(2=-x - 8\), which matches GENE's equation.

Step2: Solve GENE's equation \(2=-8 - x\)

Add \(x\) to both sides: \(2 + x=-8 - x+x\), so \(2 + x=-8\).
Subtract \(2\) from both sides: \(2 + x-2=-8 - 2\), so \(x=-10\).

Step1: Write the equation from the balance

On the left side, we have three \(x\) blocks and two \(-1\) blocks, so that's \(3x+(-1)\times2 = 3x - 2\). On the right side, we have four \(1\) blocks, so that's \(1\times4 = 4\). Since the balance is equal, the equation is \(3x-2 = 4\).

Step2: Solve the equation \(3x-2 = 4\)

Add \(2\) to both sides: \(3x-2 + 2=4 + 2\), so \(3x=6\).
Divide both sides by \(3\): \(\frac{3x}{3}=\frac{6}{3}\), so \(x = 2\).

Answer:

Circle: GENE
Solution: \(x = - 10\)

Question 12