Solve for X : $$ 3(7+2 x)+3=3(5+x)-9(x+1) $$ A $$ \frac{3}{2} $$ B $$ \frac{2}{3} $$ C $$ -\frac{2}{3} $$ D $$ -\frac{3}{2} $$

Question

UpStudy AI · Accepted Answer

Let's solve the equation step by step to find the value of $$ x $$:

$$
3(7 + 2x) + 3 = 3(5 + x) - 9(x + 1)
$$

### Step 1: Expand Both Sides

First, distribute the multiplication over addition on both sides of the equation.

**Left Side:**
$$
3(7) + 3(2x) + 3 = 21 + 6x + 3 = 24 + 6x
$$

**Right Side:**
$$
3(5) + 3(x) - 9(x) - 9(1) = 15 + 3x - 9x - 9 = 15 - 6x - 9 = 6 - 6x
$$

Now, the equation looks like this:
$$
24 + 6x = 6 - 6x
$$

### Step 2: Gather Like Terms

Bring all terms containing $$ x $$ to one side and constant terms to the other side.

$$
24 + 6x + 6x = 6
$$
$$
24 + 12x = 6
$$

### Step 3: Isolate $$ x $$

Subtract 24 from both sides to isolate the term with $$ x $$.

$$
12x = 6 - 24
$$
$$
12x = -18
$$

Now, divide both sides by 12 to solve for $$ x $$:

$$
x = \frac{-18}{12} = \frac{-3}{2} = -\frac{3}{2}
$$

### Conclusion

The value of $$ x $$ is:

**D) $$ -\frac{3}{2} $$**
$$ x = -\frac{3}{2} $$, choice D

Solve for X : \[ 3(7+2 x)+3=3(5+x)-9(x+1) \] A \( \frac{3}{2} \) B \( \frac{2}{3} \) C \( -\frac{2}{3} \) D \( -\frac{3}{2} \)