Question

directions: solve, graph, and wr -7a - 11 < 1 - 4a

Explanation:

Step1: Add 7a to both sides

To isolate the variable terms, we add \(7a\) to both sides of the inequality \(-7a - 11 < 1 - 4a\). This gives us \(-7a + 7a - 11 < 1 - 4a + 7a\), which simplifies to \(-11 < 1 + 3a\).

Step2: Subtract 1 from both sides

Next, we subtract \(1\) from both sides to get closer to isolating \(a\). So, \(-11 - 1 < 1 - 1 + 3a\), which simplifies to \(-12 < 3a\).

Step3: Divide both sides by 3

Finally, we divide both sides by \(3\) to solve for \(a\). \(\frac{-12}{3} < \frac{3a}{3}\), which simplifies to \(-4 < a\) or \(a > -4\).

Answer:

The solution to the inequality \(-7a - 11 < 1 - 4a\) is \(a > -4\). To graph this, we draw a number line, place an open circle at \(-4\) (since \(a\) is not equal to \(-4\)), and shade the region to the right of \(-4\) to represent all values of \(a\) greater than \(-4\). The solution in interval notation is \((-4, \infty)\).