1Cademy - Classifying $$4 + 9(3x - 7) = -42x - 13 + 23(3x

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Classification of Linear Equations

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Classifying $4 + 9(3x - 7) = -42x - 13 + 23(3x - 2)$

To classify the algebraic equation $4 + 9(3x - 7) = -42x - 13 + 23(3x - 2)$ , first simplify both sides. Distributing on the left side gives $4 + 27x - 63$ , which combines to $27x - 59$ . Distributing on the right side yields $-42x - 13 + 69x - 46$ . Grouping the like terms on the right ( $-42x + 69x$ and $-13 - 46$ ) also simplifies to $27x - 59$ . Equating the simplified sides results in $27x - 59 = 27x - 59$ . Subtracting $27x$ from both sides eliminates the variable entirely, leaving the unconditionally true numerical statement $-59 = -59$ . Consequently, the equation is an identity, and its solution is all real numbers.

Updated 2026-06-18

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OpenStax Intermediate Algebra

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A quality assurance inspector is comparing two different tolerance formulas for a machined part. The comparison is modeled by the equation ${}4 + 9(3x - 7) = -42x - 13 + 23(3x - 2)$ . After simplifying the expressions, the inspector finds that the variable $x$ is eliminated, leaving the true numerical statement ${}-59 = -59$ . Which mathematical term should the inspector use to classify this equation, indicating that it is true for all possible values of $x$ ?
A logistics manager setting up a supply chain model simplifies the cost equation ${}4 + 9(3x - 7) = -42x - 13 + 23(3x - 2)$ and arrives at the result $-59 = -59$ . Because this final numerical statement is always true, the manager should classify the original equation as a contradiction.
A logistics coordinator is comparing two different formulas for calculating warehouse throughput. The coordinator sets the formulas equal to each other, resulting in the equation ${}4 + 9(3x - 7) = -42x - 13 + 23(3x - 2)$ . Match each mathematical term or result with its correct description based on the simplification of this equation.
A construction estimator is verifying two different cost models by setting them equal to each other in the equation: ${}4 + 9(3x - 7) = -42x - 13 + 23(3x - 2)$ . Arrange the steps in the correct logical order to prove that this equation is an identity.
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A financial analyst is comparing two predictive models that result in the equation ${}4 + 9(3x - 7) = -42x - 13 + 23(3x - 2)$ . After distributing and combining like terms, the analyst finds that both sides simplify to the exact same expression, ${}27x - 59$ . Subtracting ${}27x$ from both sides leaves the unconditionally true numerical statement $-59 = -59$ . Recalling algebraic classifications, the analyst notes that because this equation is true for all possible values of the variable, it is cla
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