When 5 is subtracted from 2 times a number x, the result is at least 9. Which of the follo… — ACT

When $5$ is subtracted from $2$ times a number $x$ , the result is at least $9$ . Which of the following inequalities represents all possible values of $x$ ?

A
$x \leq -2$
B
$x \geq -2$
C
$x \geq 3$
$x \geq 7$ Cevap
E
$x \leq 7$

Cevap

The inequality

x \geq 7

represents all possible values of

x

The verbal statement translates to the inequality

2x - 5 \geq 9

. Adding

5

to both sides gives

2x \geq 14

, and dividing both sides by the positive number

2

results in

x \geq 7

. Since we divide by a positive number, the direction of the inequality does not change.

Adım Adım Çözüm

Translate the verbal phrase into an algebraic inequality.

2x - 5 \geq 9

'5 subtracted from 2 times a number

x

' translates to

2x - 5

, and 'at least 9' means greater than or equal to 9.

Add 5 to both sides of the inequality to isolate the variable term.

2x \geq 14

Adding 5 to both sides maintains the inequality and simplifies the left side.

Divide both sides by 2.

x \geq 7

Dividing by a positive number does not change the direction of the inequality sign.

Anahtar Kavram

Solving linear inequalities by translating verbal statements into algebraic forms and applying inverse operations.

Soru

Cevap

Adım Adım Çözüm

Anahtar Kavram

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Konular

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