Question

related questions: lesson 5: inequalities

q. select the option that makes the inequality true.

(17 - 3a > -4(6a + 1))

a. (-3)
b. (-2)
c. (-1)
d. (0)

Explanation:

Apply the distributive property

Using the Distributive Property knowledge point, expand the right side of the inequality:

$$ -4(6a + 1) = -24a - 4 $$

The inequality becomes:

$$ 17 - 3a > -24a - 4 $$

Isolate the variable terms

Using the Solving Linear Inequalities knowledge point, add \(24a\) to both sides to group the variable terms:

$$ 17 + 21a > -4 $$

Isolate the constant terms

Subtract \(17\) from both sides to isolate the variable term:

$$ 21a > -21 $$

Solve for the variable

Divide both sides by \(21\) to find the solution set:

$$ a > -1 $$

Evaluate the given options

Using the Inequality Solution Sets knowledge point, check which option satisfies \(a > -1\):

• For A: \(-3 > -1\) is False.
• For B: \(-2 > -1\) is False.
• For C: \(-1 > -1\) is False.
• For D: \(0 > -1\) is True.

Answer:

• A. -3
• B. -2
• C. -1
• D. 0 (Correct answer)