Final answer:
The correct solution interval for the inequality (3x + 21 - 2 > 3) is x > -5.3333. None of the provided options (a through d) match this interval. Therefore, the answer is that none of the provided options are correct.
Step-by-step explanation:
To solve the inequality (3x + 21) - 2 > 3, we first simplify the left side by combining like terms:
3x + 19 > 3
Next, we subtract 19 from both sides to isolate the variable term:
3x > -16
Then, we divide each side by 3 to solve for x:
x > -16/3
Converting -16/3 to a decimal, we get:
x > -5.3333...
Therefore, the correct solution interval is x > -5.3333, which is not listed in the options provided. Let's analyze the options given with respect to the actual inequality:
- a. -2.3 > x > 1 - Incorrect due to the inequality sign direction and values.
- b. x < -2.3 or x > 1 - Incorrect because x is just greater than one negative value, not less than a negative and greater than a positive value.
- c. x < 1 - Incorrect since x is greater than -5.3333.
- d. X > 2.3 - Incorrect since this does not include values between -5.3333 and 2.3.
Since none of the options match the correct answer, we would inform the student that the correct solution interval is x > -5.3333 which is not reflected in the given options.