For which values of x is the inequality 2 - 3(x + 4) \geq 11 true? — SAT

For which values of $x$ is the inequality $2 - 3(x + 4) \geq 11$ true?

$x \leq -7$ Answer
B
$x \geq -7$
C
$x \leq 1$
D
$x \leq -1$

Answer

The correct inequality is

x \leq -7

Subtracting 2 from both sides of

2 - 3(x + 4) \geq 11

gives

-3(x + 4) \geq 9

. Dividing both sides by the negative number

-3

requires reversing the inequality sign, yielding

x + 4 \leq -3

. Subtracting 4 from both sides completes the isolation of

x

, yielding the correct solution

x \leq -7

Step-by-Step Solution

Subtract 2 from both sides of the inequality.

-3(x + 4) \geq 9

This isolates the term containing the parentheses on one side of the inequality.

Divide both sides of the inequality by

-3

and reverse the direction of the inequality sign.

x + 4 \leq -3

Dividing an inequality by a negative number requires reversing the direction of the inequality symbol to maintain equivalence.

Subtract 4 from both sides of the inequality.

x \leq -7

This isolates the variable

x

on one side of the inequality, providing the final solution set.

Key Concept

Solving multi-step linear inequalities in one variable, including distributing negative constants and reversing the inequality direction when dividing by a negative number.

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Step-by-Step Solution

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