To solve the equation [tex]\(4x - 16 = 2x + 16\)[/tex], let's follow a step-by-step approach:
### Step 1: Move all terms involving [tex]\(x\)[/tex] to one side of the equation
We begin with the given equation:
[tex]\[ 4x - 16 = 2x + 16 \][/tex]
Subtract [tex]\(2x\)[/tex] from both sides to move all terms involving [tex]\(x\)[/tex] to one side:
[tex]\[ 4x - 2x - 16 = 2x - 2x + 16 \][/tex]
Simplify both sides:
[tex]\[ 2x - 16 = 16 \][/tex]
### Step 2: Move constant terms to the other side of the equation
Next, to isolate the term involving [tex]\(x\)[/tex], we add 16 to both sides:
[tex]\[ 2x - 16 + 16 = 16 + 16 \][/tex]
Simplify both sides:
[tex]\[ 2x = 32 \][/tex]
### Step 3: Solve for [tex]\(x\)[/tex]
Now, we need to solve for [tex]\(x\)[/tex]. To do this, divide both sides by 2:
[tex]\[ \frac{2x}{2} = \frac{32}{2} \][/tex]
Simplify the equation:
[tex]\[ x = 16 \][/tex]
Thus, the solution to the equation [tex]\(4x - 16 = 2x + 16\)[/tex] is:
[tex]\[ x = 16 \][/tex]
