Which of the following represents all possible values of x that satisfy the inequality -2(… — SAT

Which of the following represents all possible values of $x$ that satisfy the inequality $-2(x - 4) + 9 > 2x + 5$ ?

$x < 3$ Answer
B
$x > 3$
C
$x < -1$
D
$x < 2$

Answer

x < 3

Expanding the inequality by distributing

-2

yields

-2x + 8 + 9 > 2x + 5

, which simplifies to

-2x + 17 > 2x + 5

. Subtracting

2x

and

17

from both sides isolates the variable terms, giving

-4x > -12

. Dividing both sides by the negative coefficient

-4

and reversing the inequality sign results in the solution set representing all values of

x

less than

3

Step-by-Step Solution

Distribute the coefficient

-2

to the terms inside the parentheses on the left side of the inequality.

-2x + 8 + 9 > 2x + 5

Applying the distributive property removes the parentheses so like terms can be combined.

Combine the constant terms on the left side.

-2x + 17 > 2x + 5

Simplifying the constant terms makes it easier to isolate the variable.

Subtract

2x

and

17

from both sides of the inequality.

-4x > -12

This groups all terms containing the variable on the left side and all constant terms on the right side.

Divide both sides by

-4

and reverse the inequality sign.

x < 3

Dividing both sides of an inequality by a negative number requires reversing the direction of the inequality sign.

Key Concept

To solve a multi-step linear inequality, apply the distributive property, combine like terms, isolate the variable, and reverse the inequality sign when multiplying or dividing both sides by a negative number.

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Key Concept

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