Solve and check the following linear equation $$ 5=4(x-2)-(x-7) $$ What is the solution? Select the correct choice below and

Question

UpStudy AI · Accepted Answer

Sure, let's solve and verify the linear equation step by step:

$$
5 = 4(x - 2) - (x - 7)
$$

### Step 1: Expand the Equation

First, distribute the numbers outside the parentheses:

$$
5 = 4 \cdot x - 4 \cdot 2 - 1 \cdot x + 1 \cdot 7
$$
$$
5 = 4x - 8 - x + 7
$$

### Step 2: Combine Like Terms

Combine the terms containing $$ x $$ and the constant terms:

$$
4x - x = 3x
$$
$$
-8 + 7 = -1
$$

So, the equation simplifies to:

$$
5 = 3x - 1
$$

### Step 3: Solve for $$ x $$

Add 1 to both sides to isolate the term with $$ x $$:

$$
5 + 1 = 3x
$$
$$
6 = 3x
$$

Now, divide both sides by 3:

$$
x = \frac{6}{3}
$$
$$
x = 2
$$

### Step 4: Verify the Solution

Plug $$ x = 2 $$ back into the original equation to ensure it satisfies both sides:

$$
5 = 4(2 - 2) - (2 - 7)
$$
$$
5 = 4(0) - (-5)
$$
$$
5 = 0 + 5
$$
$$
5 = 5
$$

Since both sides are equal, $$ x = 2 $$ is the correct solution.

### **Answer:**  
$$ x = 2 $$
$$ x = 2 $$

Solve and check the following linear equation \( 5=4(x-2)-(x-7) \) What is the solution? Select the correct choice below and