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

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:** \( x = 2 \)