Question

Identify the choice that is a solution to the inequality 3/4+x<1/6 .
Responses

712
7 over 12

−712
negative 7 over 12

−12
negative 1 half

−23

Answer 1

To solve the inequality \( \frac{3}{4} + x < \frac{1}{6} \), we first isolate \( x \):

1. Subtract \( \frac{3}{4} \) from both sides:

\[
x < \frac{1}{6} - \frac{3}{4}
\]

2. To perform this subtraction, we need a common denominator. The least common multiple of 6 and 4 is 12:

\[
\frac{1}{6} = \frac{2}{12} \quad \text{and} \quad \frac{3}{4} = \frac{9}{12}
\]

3. Now we can subtract:

\[
x < \frac{2}{12} - \frac{9}{12} = \frac{2 - 9}{12} = \frac{-7}{12}
\]

Thus, the solution to the inequality is:

\[
x < -\frac{7}{12}
\]

Now we'll check the options:

- 712
- \( \frac{7}{12} \)
- \( -\frac{7}{12} \) (This is a solution since it's less than \(-\frac{7}{12}\))
- \( -12 \)
- \( -\frac{1}{2} \)
- \( -\frac{23}{12} \)

The choice that is a solution to the inequality \( 3/4 + x < 1/6 \) is:

\(-\frac{7}{12}\) (negative 7 over 12).