7(y - 2) - 4y > 5y + 10 What are all the possible values of y that satisfy the inequality … — Armed Services Vocational Aptitude Battery (ASVAB)

7(y - 2) - 4y > 5y + 10

What are all the possible values of $y$ that satisfy the inequality shown above?

$y < -12$ Answer
B
$y > -12$
C
$y < 12$
D
$y > 2$

Answer

The correct solution set is

y < -12

The correct answer is found by properly applying the distributive property, grouping like terms, isolating the variable, and correctly reversing the inequality sign when dividing by -2.

Step-by-Step Solution

Distribute the 7 to both terms inside the parentheses.

7y - 14 - 4y > 5y + 10

This clears the parentheses, allowing the variable terms to be grouped.

Combine the like terms on the left side of the inequality.

3y - 14 > 5y + 10

Subtracting

4y

from

7y

simplifies the left side to

3y

Subtract

5y

from both sides to group the variable terms on the left.

-2y - 14 > 10

This moves all terms containing

y

to one side of the inequality.

Add 14 to both sides to isolate the variable term.

-2y > 24

This leaves the

-2y

term by itself on the left side.

Divide both sides by -2 and reverse the inequality sign.

y < -12

According to the properties of inequalities, multiplying or dividing by a negative number requires flipping the direction of the inequality symbol.

Key Concept

Solving One-Variable Inequalities

Question

Answer

Step-by-Step Solution

Key Concept

Common Mistakes

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