Question
Solve for zz. Express your answer as a proper or improper fraction in simplest terms.
one half, equals, minus, start fraction, 5, divided by, 6, end fraction, minus, one quarter, z
2
1
=
−
6
5
−
4
1
z
one half, equals, minus, start fraction, 5, divided by, 6, end fraction, minus, one quarter, z
2
1
=
−
6
5
−
4
1
z
Answers
GPT-4o mini
To solve the equation
\[
\frac{1}{2} = -\frac{5}{6} - \frac{1}{4} z,
\]
we will isolate \( z \).
1. First, let's rearrange the equation to isolate the term with \( z \):
\[
\frac{1}{2} + \frac{5}{6} = -\frac{1}{4} z.
\]
2. Next, we need to combine \( \frac{1}{2} \) and \( \frac{5}{6} \). To do this, we'll find a common denominator. The least common multiple of 2 and 6 is 6. We can convert \( \frac{1}{2} \) to a fraction with a denominator of 6:
\[
\frac{1}{2} = \frac{3}{6}.
\]
3. Now we can add the fractions:
\[
\frac{3}{6} + \frac{5}{6} = \frac{3 + 5}{6} = \frac{8}{6}.
\]
4. Now we substitute back into our equation:
\[
\frac{8}{6} = -\frac{1}{4} z.
\]
5. Next, we need to isolate \( z \). To do this, we will multiply both sides by \(-4\):
\[
-4 \cdot \frac{8}{6} = z.
\]
6. Calculate \(-4 \cdot \frac{8}{6}\):
\[
z = -\frac{32}{6}.
\]
7. To simplify \(-\frac{32}{6}\), we can divide both the numerator and the denominator by their greatest common divisor (2):
\[
z = -\frac{32 \div 2}{6 \div 2} = -\frac{16}{3}.
\]
Thus, the solution for \( z \) is
\[
\boxed{-\frac{16}{3}}.
\]
\[
\frac{1}{2} = -\frac{5}{6} - \frac{1}{4} z,
\]
we will isolate \( z \).
1. First, let's rearrange the equation to isolate the term with \( z \):
\[
\frac{1}{2} + \frac{5}{6} = -\frac{1}{4} z.
\]
2. Next, we need to combine \( \frac{1}{2} \) and \( \frac{5}{6} \). To do this, we'll find a common denominator. The least common multiple of 2 and 6 is 6. We can convert \( \frac{1}{2} \) to a fraction with a denominator of 6:
\[
\frac{1}{2} = \frac{3}{6}.
\]
3. Now we can add the fractions:
\[
\frac{3}{6} + \frac{5}{6} = \frac{3 + 5}{6} = \frac{8}{6}.
\]
4. Now we substitute back into our equation:
\[
\frac{8}{6} = -\frac{1}{4} z.
\]
5. Next, we need to isolate \( z \). To do this, we will multiply both sides by \(-4\):
\[
-4 \cdot \frac{8}{6} = z.
\]
6. Calculate \(-4 \cdot \frac{8}{6}\):
\[
z = -\frac{32}{6}.
\]
7. To simplify \(-\frac{32}{6}\), we can divide both the numerator and the denominator by their greatest common divisor (2):
\[
z = -\frac{32 \div 2}{6 \div 2} = -\frac{16}{3}.
\]
Thus, the solution for \( z \) is
\[
\boxed{-\frac{16}{3}}.
\]