If -5(2x - 9) + 3 \geq 18, what is the maximum possible value of x? — SAT

If $-5(2x - 9) + 3 \geq 18$ , what is the maximum possible value of $x$ ?

Answer: 3

Answer

The correct answer is 3.

Distributing the

-5

gives

-10x + 45 + 3 \geq 18

. Combining constants yields

-10x + 48 \geq 18

. Subtracting 48 from both sides gives

-10x \geq -30

. Finally, dividing both sides by

-10

and reversing the inequality sign gives

x \leq 3

. The maximum possible value is therefore 3.

Step-by-Step Solution

Distribute

-5

to the terms inside the parentheses.

-10x + 45 + 3 \geq 18

Simplify the expression by expanding the parentheses.

Combine the constant terms

45

and

3

on the left side.

-10x + 48 \geq 18

Group like terms together.

Subtract

48

from both sides of the inequality.

-10x \geq -30

Isolate the variable term.

Divide both sides by

-10

and reverse the inequality symbol.

x \leq 3

Dividing by a negative number reverses the direction of the inequality.

Key Concept

Solving multi-step linear inequalities in one variable, applying the distributive property, and reversing the inequality sign when multiplying or dividing by a negative number.

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