Write and solve simple inequalities

An inequality represents a constraint or comparison between quantities, and the learner translates verbal conditions into one-variable forms such as $x+3<10$ or $2x\geq 8$ , then uses inverse operations to identify every value that satisfies the condition. Solutions are understood as a set, often infinitely many, and represented on a number line with appropriate open or closed endpoints; the scope is simple linear inequalities with accessible whole-number, fraction, or decimal values, not compound or nonlinear inequalities.

Detailed Explanation: Write and solve simple inequalities

An inequality compares two amounts. The symbols mean:

$<$ means “less than”
$>$ means “greater than”
$\leq$ means “less than or equal to”
$\geq$ means “greater than or equal to”

Example

A number plus 3 is less than 10. What numbers could the number be?

Step 1: Choose a variable

Let $x$ represent the number.

Step 2: Write the inequality

“Plus 3” means add $3$ , and “is less than 10” means use $<10$ :

x+3<10

Step 3: Undo the addition

Subtract $3$ from both sides:

x+3-3<10-3

So,

x<7

Step 4: Describe the solution

The answer is every number less than 7. For example, $6$ , $0$ , and $-2$ all work.

On a number line, use an open circle at $7$ because $7$ is not included, and shade to the left:

\leftarrow\!\!-\!\!-\!\!-\!\!-\!\!\circ\; \longrightarrow \qquad\quad 7

The solution is:

\boxed{x<7}

Learn by doing: Write and solve simple inequalities

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Function Domain - Simple Root of Linear to Domain Definition

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