Linear Equations UnIt IESL Score: \( 27.4 / 41 \) Answered: 14/16 Solve \( 1(x+6)-4=5(x-1) \) for \( x \) \( x=\square \) Check Answer

To solve the equation \( 1(x+6)-4=5(x-1) \), start by distributing on both sides: 1. The left side becomes \( x + 6 - 4 \), which simplifies to \( x + 2 \). 2. The right side becomes \( 5x - 5 \). Set the equation as: \( x + 2 = 5x - 5 \) Now, isolate \( x \): 3. Subtract \( x \) from both sides: \( 2 = 4x - 5 \) 4. Add 5 to both sides: \( 7 = 4x \) 5. Finally, divide by 4: \( x = \frac{7}{4} \) or \( x = 1.75 \). To check the answer, substitute \( x = 1.75 \) back into the original equation: - Left Side: \( 1(1.75 + 6) - 4 = 1(7.75) - 4 = 7.75 - 4 = 3.75 \) - Right Side: \( 5(1.75 - 1) = 5(0.75) = 3.75 \) Both sides are equal, confirming that \( x = \frac{7}{4} \) is correct! So, the final answer is: \( x = \frac{7}{4} \) or \( x = 1.75 \).