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Interpret inequality symbols in context

Inequality symbols <<, >>, \le, and \ge communicate ordered relationships between quantities: whether one is less than, greater than, or possibly equal to another. In context, the learner identifies which values satisfy a constraint, including whether the boundary value is allowed, and represents the relationship with words, numerical comparisons, or a number line; this scope does not include solving complex inequality systems or applying advanced algebraic transformations.

Detailed Explanation: Interpret inequality symbols in context

Inequality symbols compare two quantities:

  • << means less than
  • >> means greater than
  • \le means less than or equal to
  • \ge means greater than or equal to

The line underneath \le or \ge means the boundary value is allowed.

Example: A school backpack may weigh no more than 10 kilograms. What inequality describes the possible backpack weights?

Step 1: Choose a variable.
Let ww be the backpack’s weight in kilograms.

Step 2: Understand the words.
“No more than 10” means the weight can be 10 or less. The backpack may weigh exactly (10)(10) kilograms, so the boundary is included.

Step 3: Write the inequality.

w10w \le 10

This means the backpack can weigh (10)(10) kilograms or any amount less than (10)(10) kilograms. For example, 88, (9.5)(9.5), and (10)(10) satisfy the inequality, but (10.1)(10.1) does not.

On a number line, use a closed dot at (10)(10) because (10)(10) is included, and shade to the left because the weights are less than (10)(10).

Learn by doing: Interpret inequality symbols in context

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Function Domain/Range Definition - Inequality to Number Line (Without Union)


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