Answer :
Let's solve the equation step-by-step:
Given:
[tex]\[ 28x - 56 = 22x - 65 \][/tex]
### Step 1: Move variable terms to one side
We start by getting the variable [tex]\( x \)[/tex] on one side of the equation. To do this, we subtract [tex]\( 22x \)[/tex] from both sides:
[tex]\[ 28x - 22x - 56 = 22x - 22x - 65 \][/tex]
Simplifying this, we get:
[tex]\[ 6x - 56 = -65 \][/tex]
So, the first blank should be 6, as we get [tex]\( 6x - 56 = -65 \)[/tex] after subtracting [tex]\( 22x \)[/tex].
### Step 2: Isolate the variable
Now, we need to isolate the variable [tex]\( x \)[/tex]. To do this, we can add 56 to both sides of the equation:
[tex]\[ 6x - 56 + 56 = -65 + 56 \][/tex]
Simplifying this, we get:
[tex]\[ 6x = -9 \][/tex]
Using the addition property of equality, we added 56 to both sides.
### Step 3: Solve the equation
Finally, we can solve for [tex]\( x \)[/tex] by dividing both sides by 6:
[tex]\[ x = \frac{-9}{6} \][/tex]
Simplifying the fraction, we get:
[tex]\[ x = -\frac{3}{2} \][/tex] or [tex]\( x = -1.5 \)[/tex]
Thus, the second blank should be addition, as we used the addition property of equality to add 56 to both sides to isolate the variable.
### Summary
First blank: [tex]\( \boxed{6} \)[/tex]\
Second blank: [tex]\( \boxed{\text{Addition}} \)[/tex]
So, the completed description is:
First, get the variable on the left-hand side of the equation by subtracting [tex]\( 22x \)[/tex] from both sides to get [tex]\( 6x - 56 = -65 \)[/tex]. Next, use the addition property of equality to isolate the variable.
Given:
[tex]\[ 28x - 56 = 22x - 65 \][/tex]
### Step 1: Move variable terms to one side
We start by getting the variable [tex]\( x \)[/tex] on one side of the equation. To do this, we subtract [tex]\( 22x \)[/tex] from both sides:
[tex]\[ 28x - 22x - 56 = 22x - 22x - 65 \][/tex]
Simplifying this, we get:
[tex]\[ 6x - 56 = -65 \][/tex]
So, the first blank should be 6, as we get [tex]\( 6x - 56 = -65 \)[/tex] after subtracting [tex]\( 22x \)[/tex].
### Step 2: Isolate the variable
Now, we need to isolate the variable [tex]\( x \)[/tex]. To do this, we can add 56 to both sides of the equation:
[tex]\[ 6x - 56 + 56 = -65 + 56 \][/tex]
Simplifying this, we get:
[tex]\[ 6x = -9 \][/tex]
Using the addition property of equality, we added 56 to both sides.
### Step 3: Solve the equation
Finally, we can solve for [tex]\( x \)[/tex] by dividing both sides by 6:
[tex]\[ x = \frac{-9}{6} \][/tex]
Simplifying the fraction, we get:
[tex]\[ x = -\frac{3}{2} \][/tex] or [tex]\( x = -1.5 \)[/tex]
Thus, the second blank should be addition, as we used the addition property of equality to add 56 to both sides to isolate the variable.
### Summary
First blank: [tex]\( \boxed{6} \)[/tex]\
Second blank: [tex]\( \boxed{\text{Addition}} \)[/tex]
So, the completed description is:
First, get the variable on the left-hand side of the equation by subtracting [tex]\( 22x \)[/tex] from both sides to get [tex]\( 6x - 56 = -65 \)[/tex]. Next, use the addition property of equality to isolate the variable.
