Certainly! Let's solve the equation step-by-step:
### Step 1: Distribute the constants inside the parentheses
Given the equation:
[tex]\[ 4 - 2(x + 7) = 3(x + 5) \][/tex]
First, distribute [tex]\(-2\)[/tex] and [tex]\(3\)[/tex] inside their respective parentheses:
[tex]\[ 4 - 2x - 14 = 3x + 15 \][/tex]
### Step 2: Combine like terms
On the left side of the equation, combine the constant terms [tex]\(4\)[/tex] and [tex]\(-14\)[/tex]:
[tex]\[ -10 - 2x = 3x + 15 \][/tex]
### Step 3: Move the variable terms to one side
To isolate [tex]\(x\)[/tex], add [tex]\(2x\)[/tex] to both sides of the equation:
[tex]\[ -10 = 3x + 15 + 2x \][/tex]
This simplifies to:
[tex]\[ -10 = 5x + 15 \][/tex]
### Step 4: Move the constant terms to the other side
Now, subtract [tex]\(15\)[/tex] from both sides to move the constants to one side:
[tex]\[ -10 - 15 = 5x \][/tex]
This simplifies to:
[tex]\[ -25 = 5x \][/tex]
### Step 5: Solve for [tex]\(x\)[/tex]
Finally, divide both sides by [tex]\(5\)[/tex] to solve for [tex]\(x\)[/tex]:
[tex]\[ x = \frac{-25}{5} \][/tex]
This simplifies to:
[tex]\[ x = -5 \][/tex]
To verify the solution, substitute [tex]\(x = -5\)[/tex] back into the left and right sides of the original equation:
#### Left Side:
[tex]\[ 4 - 2(-5 + 7) = 4 - 2(2) = 4 - 4 = 0 \][/tex]
#### Right Side:
[tex]\[ 3(-5 + 5) = 3(0) = 0 \][/tex]
Both sides equal, so the solution satisfies the equation. Therefore, the step-by-step solution to the equation [tex]\(4 - 2(x + 7) = 3(x + 5)\)[/tex] results in:
### Solution:
[tex]\[ x = -5 \][/tex]
