Question

solve for b. express your answer as a proper or improper fraction in simplest terms.
$-\frac{1}{6} = \frac{1}{2}b + \frac{5}{6}$

Explanation:

Step1: Subtract 5/6 from both sides

To isolate the term with \( b \), we subtract \( \frac{5}{6} \) from both sides of the equation \( -\frac{1}{6} = \frac{1}{2}b + \frac{5}{6} \).

$$ -\frac{1}{6} - \frac{5}{6} = \frac{1}{2}b + \frac{5}{6} - \frac{5}{6} $$

Simplifying the left side: \( -\frac{1 + 5}{6} = -\frac{6}{6} = -1 \), and the right side simplifies to \( \frac{1}{2}b \). So we have \( -1 = \frac{1}{2}b \).

Step2: Multiply both sides by 2

To solve for \( b \), we multiply both sides of the equation \( -1 = \frac{1}{2}b \) by 2.

$$ 2 \times (-1) = 2 \times \frac{1}{2}b $$

Simplifying both sides: The left side is \( -2 \), and the right side simplifies to \( b \). So \( b = -2 \). But we can also express -2 as a fraction, \( -\frac{2}{1} \), or we can check the steps again for any miscalculations. Wait, let's re - do step 1:

Wait, \( -\frac{1}{6}-\frac{5}{6}=\frac{-1 - 5}{6}=\frac{-6}{6}=-1 \), that's correct. Then step 2: \( \frac{1}{2}b=-1 \), multiply both sides by 2: \( b=-2 \), which is \( -\frac{2}{1} \) or just -2. But let's do it using fractions throughout.

Starting over:

Given \( -\frac{1}{6}=\frac{1}{2}b+\frac{5}{6} \)

Subtract \( \frac{5}{6} \) from both sides:

\( -\frac{1}{6}-\frac{5}{6}=\frac{1}{2}b \)

\( \frac{-1 - 5}{6}=\frac{1}{2}b \)

\( \frac{-6}{6}=\frac{1}{2}b \)

\( - 1=\frac{1}{2}b \)

Multiply both sides by 2:

\( b=-2=-\frac{2}{1} \)

Answer:

\( b = -\frac{2}{1} \) (or \( b=-2 \))