Solve and check the linear equation. $$ 3(x-4)+15=2(x+5) $$

Question

UpStudy AI · Accepted Answer

To solve and verify the linear equation:

$$
3(x - 4) + 15 = 2(x + 5)
$$

let's follow these steps:

### Step 1: Expand Both Sides

**Left Side:**
$$
3(x - 4) + 15 = 3x - 12 + 15 = 3x + 3
$$

**Right Side:**
$$
2(x + 5) = 2x + 10
$$

So, the equation becomes:
$$
3x + 3 = 2x + 10
$$

### Step 2: Gather Like Terms

Subtract $$2x$$ from both sides to get all $$x$$ terms on one side:
$$
3x + 3 - 2x = 2x + 10 - 2x
$$
$$
x + 3 = 10
$$

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

Subtract 3 from both sides to solve for $$x$$:
$$
x + 3 - 3 = 10 - 3
$$
$$
x = 7
$$

### Solution

$$
x = 7
$$

### Step 4: Check the Solution

Substitute $$x = 7$$ back into the original equation to verify:

$$
3(7 - 4) + 15 = 2(7 + 5)
$$

**Calculate Both Sides:**

**Left Side:**
$$
3(3) + 15 = 9 + 15 = 24
$$

**Right Side:**
$$
2(12) = 24
$$

Since both sides equal 24, the solution $$x = 7$$ is correct.
$$ x = 7 $$

Solve and check the linear equation.