If -2(x - 5) \geq 4, what is the maximum possible value of x? — SAT

If $-2(x - 5) \geq 4$ , what is the maximum possible value of $x$ ?

Answer: 3

Distributing the

-2

on the left side of the inequality

-2(x - 5) \geq 4

yields

-2x + 10 \geq 4

. Subtracting

10

from both sides gives

-2x \geq -6

. Dividing both sides by

-2

and reversing the inequality sign results in

x \leq 3

. The maximum possible value is therefore 3.

Distribute

-2

to the terms inside the parentheses.

-2x + 10 \geq 4

Applying the distributive property simplifies the inequality.

Subtract

10

from both sides of the inequality.

-2x \geq -6

This isolates the variable term on the left side.

Divide both sides of the inequality by

-2

and reverse the inequality sign.

x \leq 3

Dividing both sides of an inequality by a negative number reverses the direction of the inequality.

Solving linear inequalities in one variable using the distributive property and division by negative numbers.

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