Question

solve the inequality. graph the solution set, and write the solution set in set - builder notation and interval notation. write numbers as simplified fractions or integers. -7a + 3 > 59
part: 0 / 3
part 1 of 3
the solution set in set - builder notation is

Explanation:

Step1: Subtract 3 from both sides

To isolate the term with \(a\), we subtract 3 from both sides of the inequality \(-7a + 3>59\). This gives us \(-7a+3 - 3>59 - 3\), which simplifies to \(-7a>56\).

Step2: Divide by -7 (reverse inequality)

When we divide both sides of an inequality by a negative number, we must reverse the inequality sign. So, dividing both sides of \(-7a>56\) by \(-7\) gives \(a <\frac{56}{-7}\), which simplifies to \(a < - 8\).

Step3: Write in set - builder notation

The set - builder notation for all real numbers \(a\) such that \(a\) is less than \(-8\) is \(\{a\in\mathbb{R}\mid a < - 8\}\).

Answer:

\(\{a\in\mathbb{R}\mid a < - 8\}\)