Question

interactive practice: write and solve one - variable equations
use the hanger to solve an equation.
how can you get ( x ) by itself and keep the
hanger balanced?
? ? on both sides.
( x + 2 = 5 )

Explanation:

Step1: Analyze the hanger equation

The hanger represents the equation \(x + 2 = 5\) (wait, actually looking at the hanger: left side is \(x + 2\) (x and two 1s)? Wait no, the left side has x and two 1s? Wait the image shows left side: x, then two 1s? Wait no, the equation at the bottom is \(x + 2 = 5\)? Wait no, looking at the hanger: left side has x and two 1s? Wait the right side has five 1s? Wait no, the right side has five 1s? Wait the left side: x, then two 1s? Wait the equation should be \(x + 2 = 5\)? Wait to solve for x, we need to isolate x. The principle is that to keep the hanger balanced, we do the same operation to both sides. So we need to remove the 2 (the two 1s) from the left side. So we subtract 2 (or remove two 1s) from both sides. Wait the question is "How can you get x by itself and keep the hanger balanced?" So the operation is to subtract 2 (or remove two 1s) from both sides. Wait the drop - down boxes: first box is the operation, second is the number. So the operation is "subtract" and the number is "2". Wait let's correct: the left side has x + 2 (x and two 1s), right side has 5 (five 1s). To isolate x, we need to remove the two 1s from the left side. So we do the same to the right side: remove two 1s. So the operation is "subtract" and the number is "2". So step 1: Identify the equation from the hanger: \(x + 2=5\). Step 2: To isolate x, we use the subtraction property of equality: subtract 2 from both sides. So the first drop - down is "subtract" and the second is "2".

Step2: Confirm the operation

The hanger is balanced, so whatever we do to one side, we must do to the other. The left side has \(x\) plus 2 (the two 1 - unit weights). To get \(x\) alone, we need to remove the 2 unit weights. So we subtract 2 from both sides. This keeps the hanger balanced because we are removing the same amount of weight from both sides.

Answer:

The first drop - down should be "subtract" and the second drop - down should be "2" (i.e., subtract 2 on both sides).