How to Solve One-Step Inequalities

How to Solve One-Step Inequalities?

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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.

Free printable Worksheets

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: $x \ - \ 26 \ < \ -31$

Answers

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

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

One Step Inequalities

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

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

One Step Inequalities2

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

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

One Step Inequalities3

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

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

One Step Inequalities4

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

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

One Step Inequalities5

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

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

One Step Inequalities6

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

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

One Step Inequalities7

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

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

One Step Inequalities

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

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

One Step Inequalities9

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

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

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How to Solve One-Step Inequalities