ich best describes the equation (Enter then (1)/(2)(8x+5)-6=5(x-1)

To solve the equation \(\frac{1}{2}(8x+5)-6=5(x-1)\), we need to follow these steps:<br /><br />1. Distribute the \(\frac{1}{2}\) on the left side of the equation.<br />2. Simplify both sides of the equation.<br />3. Isolate the variable \(x\).<br /><br />Let's go through these steps in detail:<br /><br />### Step 1: Distribute the \(\frac{1}{2}\)<br />\[<br />\frac{1}{2}(8x + 5) - 6 = 5(x - 1)<br />\]<br />Distribute \(\frac{1}{2}\):<br />\[<br />\frac{1}{2} \cdot 8x + \frac{1}{2} \cdot 5 - 6 = 5(x - 1)<br />\]<br />\[<br />4x + \frac{5}{2} - 6 = 5(x - 1)<br />\]<br /><br />### Step 2: Simplify both sides of the equation<br />Combine like terms on the left side:<br />\[<br />4x + \frac{5}{2} - 6 = 5(x - 1)<br />\]<br />Convert 6 to a fraction with a denominator of 2:<br />\[<br />4x + \frac{5}{2} - \frac{12}{2} = 5(x - 1)<br />\]<br />Combine the fractions:<br />\[<br />4x - \frac{7}{2} = 5(x - 1)<br />\]<br /><br />Distribute 5 on the right side:<br />\[<br />4x - \frac{7}{2} = 5x - 5<br />\]<br /><br />### Step 3: Isolate the variable \(x\)<br />Move all terms involving \(x\) to one side and constants to the other side:<br />\[<br />4x - 5x = -5 + \frac{7}{2}<br />\]<br />Combine like terms:<br />\[<br />-x = -5 + \frac{7}{2}<br />\]<br />Convert -5 to a fraction with a denominator of 2:<br />\[<br />-x = -\frac{10}{2} + \frac{7}{2}<br />\]<br />Combine the fractions:<br />\[<br />-x = -\frac{3}{2}<br />\]<br /><br />Multiply both sides by -1 to solve for \(x\):<br />\[<br />x = \frac{3}{2}<br />\]<br /><br />So, the solution to the equation is:<br />\[<br />x = \frac{3}{2}<br />\]