Let's solve the equation step-by-step:
Given equation:
[tex]\[
\frac{-3x - 7}{4} = 11
\][/tex]
### Step 1: Multiplication Property of Equality
To eliminate the fraction, we multiply both sides of the equation by 4:
[tex]\[
\frac{-3x - 7}{4} \cdot 4 = 11 \cdot 4
\][/tex]
[tex]\[
-3x - 7 = 44
\][/tex]
### Step 2: Simplification
The equation is now:
[tex]\[
-3x - 7 = 44
\][/tex]
### Step 3: Addition Property of Equality
To isolate the term with [tex]\( x \)[/tex], we add 7 to both sides:
[tex]\[
-3x - 7 + 7 = 44 + 7
\][/tex]
[tex]\[
-3x = 51
\][/tex]
### Step 4: Simplification
The equation now is:
[tex]\[
-3x = 51
\][/tex]
### Step 5: Division Property of Equality
To solve for [tex]\( x \)[/tex], we divide both sides by -3:
[tex]\[
\frac{-3x}{-3} = \frac{51}{-3}
\][/tex]
[tex]\[
x = -17
\][/tex]
### Step 6: Simplification
The final result is:
[tex]\[
x = -17
\][/tex]
So, the value of [tex]\( x \)[/tex] is [tex]\( -17 \)[/tex].
Here is the completed table with justifications for each step:
[tex]\[
\begin{array}{|r|ll}
\hline
\text{Steps} & \text{Justifications} \\
\hline
\frac{-3x - 7}{4} \cdot 4 = 11 \cdot 4 & \text{1. Multiplication property of equality} \\
-3x - 7 = 44 & \text{2. Simplification} \\
-3x - 7 + 7 = 44 + 7 & \text{3. Addition property of equality} \\
-3x = 51 & \text{4. Simplification} \\
\frac{-3x}{-3} = \frac{51}{-3} & \text{5. Division property of equality} \\
x = -17 & \text{6. Simplification} \\
\hline
\end{array}
\][/tex]
