## How to Solve One-Step Inequalities

Read,5 minutes

The term inequality signifies a mathematical expression where the sides **aren’t** the **same.** Essentially, there are 5 inequality **symbols **utilized for representing equations of inequality, which are:

**less**than (\(<\)),**greater**than (\(>\)),**less**than or**equal**(\(≤\)),**greater**than or**equal**(\(≥\))- and the
**not equal**symbol (\(≠\)).

Inequalities are utilized for **comparing **numbers and **determining** the **range** or ranges of the values which meet the given variable’s **conditions.**

### How do you Solve Single-step Inequalities?

Solving single-step inequalities is a clear-cut process just like it sounds. There is merely a single step needed for completely solving these equations.

The **chief** objective of solving a one-step inequality is to first **isolate **a variable on one side of the inequality symbol and then make its **coefficient** equal to **one.**

The tactic for **isolating** a variable involves using **opposite operations.** For example, to move a number you **subtracted** from the other side of the inequality, you must **add.**

The top **vital step** not to forget whenever solving any kind of linear or inequality equations is to do the **same operation** for both the **right-hand** side as well as the **left-hand** side of an equation.

So, if one subtracts or adds from one side of the inequality, they also **have** to subtract or add with the **exact same** value from the other side. Likewise, if one multiplies or divides on one side of an equation, they also have to multiply or divide using the **same value** on the equation’s other side.

The sole exception whenever dividing and multiplying using a **negative number** in the inequality equation is that the inequality **symbol** is **reversed.**

Here is a **summary** of the **rules** you must use to solve one-step inequalities:

**Subtracting**or**adding**the**exact same**number from both sides of an inequality ends up with the inequality symbol**not changing.****Dividing**or**multiplying**both sides via a**positive**number ends up with the inequality symbol**not changing.****Multiplying**or**dividing**both sides using a**negative**number will**change**the inequality. This infers, \(<\) changes to \(>\), and**vice-versa**.

### Exercises for One-Step Inequalities

**1) **Draw a graph for: \(x \ + \ 5 \ < \ 1\)

**2) **Draw a graph for: \(x \ + \ 6 \ > \ 4\)

**3) **Draw a graph for: \(x \ - \ 7 \ ≤ \ -8\)

**4) **Draw a graph for: \(x \ + \ 11 \ ≥ \ 6\)

**5) **Draw a graph for: \(x \ + \ 31 \ > \ 29\)

**6) **Draw a graph for: \(x \ - \ 67 \ < \ -66\)

**7) **Draw a graph for: \(x \ + \ 10 \ ≥ \ 7\)

**8) **Draw a graph for: \(x \ + \ 13 \ ≤ \ 11\)

**9) **Draw a graph for: \(x \ + \ 17 \ > \ 13\)

**10) **Draw a graph for: \(x \ - \ 26 \ < \ -31\)

**1) **Draw a graph for: \(x \ + \ 5 \ < \ 1\)

\(\color{red}{x \ + \ 5 \ < \ 1 \ ⇒ \ x \ < \ -4}\)

**2) **Draw a graph for: \(x \ + \ 6 \ > \ 4\)

\(\color{red}{x \ + \ 6 \ > \ 4 \ ⇒ \ x \ > \ -2}\)

**3) **Draw a graph for: \(x \ - \ 7 \ ≤ \ -8\)

\(\color{red}{x \ - \ 7 \ ≤ \ -8 \ ⇒ \ x \ ≤ \ -1}\)

**4) **Draw a graph for: \(x \ + \ 11 \ ≥ \ 6\)

\(\color{red}{x \ + \ 11 \ ≥ \ 6 \ ⇒ \ x \ ≥ \ -5}\)

**5) **Draw a graph for: \(x \ + \ 31 \ > \ 29\)

\(\color{red}{x \ + \ 31 \ > \ 29 \ ⇒ \ x \ > \ -2}\)

**6) **Draw a graph for: \(x \ - \ 67 \ < \ -66\)

\(\color{red}{x \ - \ 67 \ < \ -66 \ ⇒ \ x \ < \ 1}\)

**7) **Draw a graph for: \(x \ + \ 10 \ ≥ \ 7\)

\(\color{red}{x \ + \ 10 \ ≥ \ 7 \ ⇒ \ x \ ≥ \ -3}\)

**8) **Draw a graph for: \(x \ + \ 13 \ ≤ \ 11\)

\(\color{red}{x \ + \ 13 \ ≤ \ 11 \ ⇒ \ x \ ≤ \ -2}\)

**9) **Draw a graph for: \(x \ + \ 17 \ > \ 13\)

\(\color{red}{x \ + \ 17 \ > \ 13 \ ⇒ \ x \ > \ -4}\)

**10) **Draw a graph for: \(x \ - \ 26 \ < \ -31\)

\(\color{red}{x \ - \ 26 \ < \ -31 \ ⇒ \ x \ < \ -5}\)