A student needs to solve the following algebraic inequality: 7 - 2(x - 3) \geq 4x - 5 What… — Armed Services Vocational Aptitude Battery (ASVAB)

A student needs to solve the following algebraic inequality:

7 - 2(x - 3) \geq 4x - 5

What is the correct solution for $x$ ?

The correct solution is

x \leq 3

The correct answer is derived by carefully distributing the

-2

, combining the constants, grouping the variables on one side, and dividing by

-6

. Crucially, dividing by a negative coefficient triggers the rule to flip the

\geq

sign to

\leq

, resulting in

x \leq 3

Distribute the

-2

into the parentheses on the left side of the inequality.

7 - 2x + 6 \geq 4x - 5

To eliminate the parentheses and allow like terms to be combined.

Combine the constant terms on the left side.

13 - 2x \geq 4x - 5

Adding

7

and

6

simplifies the left side of the algebraic expression.

Subtract

4x

from both sides of the inequality.

13 - 6x \geq -5

To group all terms containing the variable

x

onto the left side.

Subtract

13

from both sides.

-6x \geq -18

To isolate the variable term on one side and the constant values on the other.

Divide both sides by

-6

and reverse the inequality symbol.

x \leq 3

Whenever an inequality is multiplied or divided by a negative number, the direction of the inequality sign must be flipped.

Solving multi-step inequalities, including the distributive property and the inequality flip rule for negative coefficients.

Question