Question

for each value of w, determine whether it is a solution to 55 < -9w + 1.
w
is it a solution?
yes no
-6
1
5
-10

Explanation:

Step1: Solve the inequality for \( w \)

Start with \( 55 < -9w + 1 \). Subtract 1 from both sides:
\( 55 - 1 < -9w + 1 - 1 \)
\( 54 < -9w \)

Divide both sides by -9 (remember to reverse the inequality sign when dividing by a negative number):
\( \frac{54}{-9} > \frac{-9w}{-9} \)
\( -6 > w \) or \( w < -6 \)

Step2: Check each value of \( w \)

• For \( w = -6 \):

The inequality is \( w < -6 \). Since \( -6 \) is not less than \( -6 \), \( -6 \) is not a solution.

• For \( w = 1 \):

\( 1 < -6 \) is false, so 1 is not a solution.

• For \( w = 5 \):

\( 5 < -6 \) is false, so 5 is not a solution.

• For \( w = -10 \):

\( -10 < -6 \) is true, so \( -10 \) is a solution.

Answer:

\( w \)	Is it a solution?
1	No
5	No
-10	Yes

(Note: In the table, mark "Yes" for \( w = -10 \) and "No" for \( w = -6 \), \( w = 1 \), \( w = 5 \).)