One Step Inequalities

Single-step inequalities or One step inequalities are mathematical expressions that involve a comparison between two quantities using an inequality symbol.

Table of Contents:

• One Step Inequalities
• How to Solve Single-step Inequalities?
• Solved Examples
• FAQs

One Step Inequalities

Single-step inequalities or One step inequalities are mathematical expressions that involve a comparison between two quantities using an inequality symbol. The goal is to determine the range of values that satisfy the given inequality.

Here are the common inequality symbols used in single-step inequalities:

• Greater than: (>)
• Less than: (<)
• Greater than or equal to: (≥)
• Less than or equal to: (≤)

How to Solve Single-step Inequalities?

1. Start by isolating the variable term on one side of the inequality. Treat it just like solving an equation. Use inverse operations to move terms to the opposite side of the inequality sign.

2. Perform the same operation on both sides of the inequality to maintain the inequality’s integrity. Remember to reverse the inequality sign if you multiply or divide both sides by a negative number.

3. Simplify the expression and obtain the solution for the variable. This will give you the range of values that satisfy the inequality.

4. Represent the solution on a number line or in interval notation.

Solved Examples

Q1: Solve the inequality 2x + 3 > 7.

1. Start with the given inequality: 2x + 3 > 7.

2. To isolate the variable term, subtract 3 from both sides:

2x + 3 – 3 > 7 – 3.

2x > 4

3. Perform the same operation on both sides. Divide both sides by 2 to solve for x:

(2x)/2 > 4/2.

x > 2.

4. The solution is x > 2, meaning any value of x greater than 2 will satisfy the inequality.

Q2: Solve the inequality 5 – 3x ≤ 8.

1. Start with the given inequality: 5 – 3x ≤ 8.

2. To isolate the variable term, subtract 5 from both sides:

5 – 3x – 5 ≤ 8 – 5.

-3x ≤ 3.

3. Perform the same operation on both sides. Divide both sides by -3, remembering to reverse the inequality sign:

(-3x)/-3 ≥ 3/-3.

x ≥ -1.

4. The solution is x ≥ -1, meaning any value of x greater than or equal to -1 will satisfy the inequality.

Q3: Solve the inequality 6 + 2x < 14.

1. Start with the given inequality: 6 + 2x < 14.

2. To isolate the variable term, subtract 6 from both sides:

6 + 2x – 6 < 14 – 6.

2x < 8.

3. Perform the same operation on both sides. Divide both sides by 2 to solve for x:

(2x)/2 < 8/2.

x < 4.

4. The solution is x < 4, meaning any value of x less than 4 will satisfy the inequality.

One Step Inequalities FAQS

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