Solve for a.

a–4 / 4 <0 or a–6≥7
Write your answer as a compound inequality with integers.

1 answer

To solve the inequalities \( \frac{a - 4}{4} < 0 \) and \( a - 6 \geq 7 \), we'll solve each part separately and then combine the results.

  1. Solving the first inequality:

\[ \frac{a - 4}{4} < 0 \]

To eliminate the fraction, multiply both sides by 4 (note that 4 is positive, so the inequality direction stays the same).

\[ a - 4 < 0 \]

Now, add 4 to both sides:

\[ a < 4 \]

  1. Solving the second inequality:

\[ a - 6 \geq 7 \]

Add 6 to both sides:

\[ a \geq 13 \]

  1. Combining the results:

The solution to the inequalities is:

\[ a < 4 \quad \text{or} \quad a \geq 13 \]

In interval notation, this can be expressed as:

\[ (-\infty, 4) \cup [13, \infty) \]

Summarizing, the answer in terms of compound inequality with integers is:

\[ a < 4 \quad \text{or} \quad a \geq 13 \]