Which of the following describes the correct solution set for the inequality -2x - 3 \leq … — Armed Services Vocational Aptitude Battery (ASVAB)

Which of the following describes the correct solution set for the inequality $-2x - 3 \leq 9$ ?

$x \geq -6$ Cevap
B
$x \leq -6$
C
$x \geq 6$
D
$x \leq 6$

Cevap

The correct solution is

x \geq -6

To solve the inequality, first isolate the variable term by adding 3 to both sides, which simplifies to

-2x \leq 12

. Next, divide both sides by -2. A critical rule of inequalities is that dividing or multiplying by a negative number requires reversing the inequality symbol. Therefore,

\leq

becomes

\geq

, and

12 \div -2 = -6

, resulting in the final answer of

x \geq -6

Adım Adım Çözüm

Isolate the variable term by adding 3 to both sides of the inequality.

-2x \leq 12

This removes the constant term from the side with the variable, leaving only the term with x.

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

x \geq -6

When multiplying or dividing an inequality by a negative number, the direction of the inequality must flip to keep the mathematical statement true.

Anahtar Kavram

Solving one-variable inequalities and applying the inequality flip rule.

Tahmini Süre:45s

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Cevap

Adım Adım Çözüm

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