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
$x \geq 3$
$x \geq 7$ Answer
E
$x \leq 7$

Answer

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.

Step-by-Step Solution

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.

Key Concept

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

Question

Answer

Step-by-Step Solution

Key Concept

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