Let's solve the given equation step-by-step.
The given equation is:
[tex]\[ 4 + 1x = 3(9 + x) \][/tex]
### Step 1: Distribute the 3 on the right side of the equation
Apply the distributive property to the right-hand side:
[tex]\[ 3(9 + x) = 3 \cdot 9 + 3 \cdot x = 27 + 3x \][/tex]
After distributing, the equation looks like:
[tex]\[ 4 + x = 27 + 3x \][/tex]
### Step 2: Move x terms to one side and constants to the other side
To simplify the equation, move the [tex]\( x \)[/tex]-terms to one side and the constants to the other side. Subtract [tex]\( x \)[/tex] from both sides to get rid of [tex]\( x \)[/tex] on the left:
[tex]\[ 4 + x - x = 27 + 3x - x \][/tex]
This simplifies to:
[tex]\[ 4 = 27 + 2x \][/tex]
Next, subtract 27 from both sides to isolate the [tex]\( x \)[/tex]-terms:
[tex]\[ 4 - 27 = 2x \][/tex]
This simplifies to:
[tex]\[ -23 = 2x \][/tex]
### Step 3: Solve for [tex]\( x \)[/tex]
Finally, divide both sides by 2 to isolate [tex]\( x \)[/tex]:
[tex]\[ x = \frac{-23}{2} \][/tex]
This simplifies to:
[tex]\[ x = -11.5 \][/tex]
Thus, the solution to the equation [tex]\( 4 + 1x = 3(9 + x) \)[/tex] is:
[tex]\[ x = -11.5 \][/tex]
