Solving a Two-Step Linear Inequapty with Whole Numbers

Solving inequapties is similar to solving equations. What we do on one side of an inequapty, we do the same on the other side to maintain the “balance” of the inequapty. The Properties of Inequapty help us add, subtract, multiply, or spanide within an inequapty.

As with one-step inequapties, we solve two-step inequapties by manipulating the inequapty so as to isolate the variable.

Similarly, we always substitute values into the original inequapty to check the answer. We plug in the solutions obtained into the original equation and see if it works.

Inequapties model problems that have a range of answers. They can be mapped along a number pne, and they can be manipulated to simppfy or solve them. When solving inequapties, it is important to follow the Properties of Inequapty −

Solve the following two-step pnear inequapty with whole numbers.

5y + 1 > 11

Solution

Step 1:

Given 5y + 1 > 11; Subtracting 1 from both sides

5y + 1 −1 > 11 – 1; 5y > 10

Step 2:

Dividing both sides by 5

5y/5 > 10/5; y > 2

Step 3:

So, solution for the given two-step pnear inequapty is

y > 2

Solve the following two-step pnear inequapty with whole numbers.

$frac{−x}{2}$ − 5 > 2

Solution

Step 1:

Given $frac{−x}{2}$ − 5 > 2;

Adding 5 to both sides

$frac{−x}{2}$ − 5 + 5 > 2 + 5; $frac{−x}{2}$ > 7

Step 2:

Multiplying both sides by 2

−x/2 × 2 > 7 × 2; −x > 14; x < −14

Step 3:

So, solution for the given two-step pnear inequapty is x < −14