\( (x \) Solve for \( x: \) \( x(8+2)+3=2(5+x)+5(x+1)-6 \) \( 4 \times \quad \) A -4 \( 4 \times \quad \) C \( \quad 2 \) \( 4 x \quad 2 \)

To solve the equation \( x(8+2)+3=2(5+x)+5(x+1)-6 \), we begin by simplifying both sides. First, rewrite it: \[ 10x + 3 = 10 + 2x + 5x + 5 - 6 \] On the right side: \[ 10x + 3 = 10 + 7x - 6 \] This simplifies to: \[ 10x + 3 = 4 + 7x \] Next, we isolate \( x \). Subtract \( 7x \) from both sides: \[ 10x - 7x + 3 = 4 \] This gives us: \[ 3x + 3 = 4 \] Now, subtract 3 from both sides: \[ 3x = 1 \] Finally, divide by 3: \[ x = \frac{1}{3} \] This solution can then be checked by substituting \( \frac{1}{3} \) back into the original equation. To ensure everything’s clear, let’s summarize a couple of insightful points. From ancient Babylon to modern classrooms, solving equations like this is rooted in mathematics history! The basics of algebra were documented over 4,000 years ago, and here we are still unraveling their mysteries today! In real-world applications, algebra isn’t just for classrooms; it’s used in fields like engineering and economics! For instance, engineers often solve equations to determine forces acting on structures, ensuring your skyscraper is both tall and stable. Solving for \( x \) could potentially save lives!