Which of the following describes all values of x that satisfy the inequality below? 2(x - … — Armed Services Vocational Aptitude Battery (ASVAB)

Which of the following describes all values of $x$ that satisfy the inequality below?

2(x - 4) - 5x < x + 4

$x > -3$ Answer
B
$x < -3$
C
$x > 3$
D
$x > 1$

Answer

The correct solution is

x > -3

The correct answer accurately simplifies the equation down to

-4x < 12

. Because isolating the variable in the final step requires dividing by

-4

, the less than symbol (

<

) must be reversed to a greater than symbol (

>

), resulting in

x > -3

Step-by-Step Solution

Distribute the 2 into the parentheses on the left side.

2x - 8 - 5x < x + 4

To clear the parentheses and access the terms inside.

Combine the like terms (

2x

and

-5x

) on the left side.

-3x - 8 < x + 4

To simplify the left side of the inequality.

Subtract

x

from both sides to group the variable terms.

-4x - 8 < 4

To collect all terms containing

x

on one side.

Add 8 to both sides of the inequality.

-4x < 12

To isolate the term with the variable.

Divide both sides by -4 and reverse the inequality sign.

x > -3

When multiplying or dividing an inequality by a negative number, the inequality symbol must be flipped to maintain a mathematically true statement.

Key Concept

Solving linear inequalities with variables on both sides requires combining like terms and reversing the inequality symbol when dividing by a negative coefficient.

Question

Answer

Step-by-Step Solution

Key Concept

Common Mistakes

Topics

More questions from this topic