Consider the following one-variable inequality: 12 - 3x \leq 27 Which of the following rep… — Armed Services Vocational Aptitude Battery (ASVAB)

Consider the following one-variable inequality:

12 - 3x \leq 27

Which of the following represents the correct solution set for $x$ ?

$x \geq -5$ Cevap
B
$x \leq -5$
C
$x \geq 5$
D
$x \geq -13$

Cevap

x \geq -5

To solve the inequality, first subtract 12 from both sides to get

-3x \leq 15

. Next, divide both sides by -3. Because the division involves a negative number, the direction of the inequality symbol must be reversed, resulting in the correct solution of

x \geq -5

Adım Adım Çözüm

Subtract

12

from both sides of the inequality.

-3x \leq 15

This step isolates the term containing the variable on one side of the inequality.

Divide both sides by

-3

and reverse the inequality symbol.

x \geq -5

According to the rules of algebra, whenever you multiply or divide an inequality by a negative number, the direction of the inequality sign must be flipped.

Anahtar Kavram

Solving One-Variable Inequalities

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