9. $$ 3(2x-5)+2(4x+7)=5(3x+1) $$

Question

UpStudy AI · Accepted Answer

Let's solve the equation step by step:

$$
3(2x - 5) + 2(4x + 7) = 5(3x + 1)
$$

### Step 1: Expand the Parentheses

Multiply each term inside the parentheses by the factor outside:

$$
3 \cdot 2x + 3 \cdot (-5) + 2 \cdot 4x + 2 \cdot 7 = 5 \cdot 3x + 5 \cdot 1
$$

This simplifies to:

$$
6x - 15 + 8x + 14 = 15x + 5
$$

### Step 2: Combine Like Terms

Combine the $$x$$ terms and the constant terms on the left side:

$$
(6x + 8x) + (-15 + 14) = 15x + 5
$$

$$
14x - 1 = 15x + 5
$$

### Step 3: Get All $$x$$ Terms on One Side

Subtract $$14x$$ from both sides to get the $$x$$ terms on one side:

$$
14x - 1 - 14x = 15x + 5 - 14x
$$

$$
-1 = x + 5
$$

### Step 4: Isolate $$x$$

Subtract 5 from both sides to solve for $$x$$:

$$
-1 - 5 = x
$$

$$
-6 = x
$$

### Conclusion

The solution to the equation is:

$$
x = -6
$$
$$ x = -6 $$

Solución de inteligencia artificial de Upstudy