Subjects algebra

Inequality Components

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1. The problem is to analyze the inequality $$-54r + 40c - 50w - 94n + 74a - 36 < 489$$ and identify its components. 2. A **coefficient** is the numerical factor multiplying a variable. For example, in $$-54r$$, the coefficient is $$-54$$. 3. A **variable** is a symbol representing an unknown value. Here, the variables are $$r, c, w, n, a$$. 4. A **term** is a product of a coefficient and a variable or a constant alone. Terms here include $$-54r, 40c, -50w, -94n, 74a,$$ and $$-36$$. 5. A **constant** is a term without a variable, here $$-36$$. 6. An **expression** is a combination of terms without an equality or inequality sign. The left side $$-54r + 40c - 50w - 94n + 74a - 36$$ is an expression. 7. An **equation** is a statement that two expressions are equal, using $$=$$. This problem is not an equation. 8. An **inequality** compares two expressions using inequality signs like $$<, >, \leq, \geq$$. Here, the inequality is $$-54r + 40c - 50w - 94n + 74a - 36 < 489$$. Final answer: The inequality consists of coefficients $$-54, 40, -50, -94, 74$$, variables $$r, c, w, n, a$$, terms $$-54r, 40c, -50w, -94n, 74a, -36$$, constant $$-36$$, expression $$-54r + 40c - 50w - 94n + 74a - 36$$, and inequality $$-54r + 40c - 50w - 94n + 74a - 36 < 489$$.