Question

for each value of x, determine whether it is a solution to x - 28 < 8.
(a) is x = 41 a solution?
yes no
(b) is x = 31 a solution?
yes no
(c) is x = 40 a solution?
yes no
(d) is x = 37 a solution?
yes no

Explanation:

To determine if a value of \( x \) is a solution to the inequality \( x - 28 < 8 \), we can first solve the inequality for \( x \) or substitute the value of \( x \) into the inequality and check if the statement is true.

Step 1: Solve the inequality \( x - 28 < 8 \)

Add 28 to both sides of the inequality:

$$ x - 28 + 28 < 8 + 28 $$

$$ x < 36 $$

So, any \( x \) value less than 36 is a solution.

Step 2: Check each value of \( x \)

(a) \( x = 41 \)

Since \( 41 \) is not less than \( 36 \) (because \( 41 > 36 \)), \( x = 41 \) is not a solution.

(b) \( x = 31 \)

Since \( 31 \) is less than \( 36 \) (because \( 31 < 36 \)), \( x = 31 \) is a solution.

(c) \( x = 40 \)

Since \( 40 \) is not less than \( 36 \) (because \( 40 > 36 \)), \( x = 40 \) is not a solution.

(d) \( x = 37 \)

Since \( 37 \) is not less than \( 36 \) (because \( 37 > 36 \)), \( x = 37 \) is not a solution.

Answer:

(a) No
(b) Yes
(c) No
(d) No