Question

Solve the inequality.
To solve the inequality, start by finding the value of g that makes 9g+32=95 true.
9g+32 < 95
9g+32
=
95

g
=
Good work!
7 is the solution to the equation and the boundary point, or the point that separates numbers that are solutions to the inequality from numbers that are not solutions. Use the solution to the equation to solve the inequality.
9g+32 < 95
g



9g+32 = 95
g = 7

Answer 1

To solve the inequality \(9g + 32 < 95\), we first solve the corresponding equation to find the boundary point.

The corresponding equation is:

\[
9g + 32 = 95
\]

Now, let's isolate \(g\):

1. Subtract 32 from both sides:

\[
9g = 95 - 32
\]

\[
9g = 63
\]

2. Divide both sides by 9:

\[
g = \frac{63}{9}
\]

\[
g = 7
\]

Now that we have \(g = 7\) as the boundary point, we can proceed to solve the inequality. The inequality we need to solve is:

\[
9g + 32 < 95
\]

Using the boundary point \(g = 7\), we will determine which side of this point satisfies the inequality.

1. **Test a value less than \(7\)** (for example, \(g = 6\)):

\[
9(6) + 32 = 54 + 32 = 86
\]

Since \(86 < 95\), \(g = 6\) is a solution.

2. **Test a value greater than \(7\)** (for example, \(g = 8\)):

\[
9(8) + 32 = 72 + 32 = 104
\]

Since \(104 > 95\), \(g = 8\) is not a solution.

Since the inequality is strict (less than and not less than or equal to), the solution set is all values of \(g\) that are less than \(7\).

Therefore, the solution to the inequality \(9g + 32 < 95\) is:

\[
g < 7
\]

In interval notation, this can be written as:

\[
(-\infty, 7)
\]