CONCEPT PREVIEW Which one is not a linear equation? A. 5x + 7 (x - 1) = -3x B. 9x² - 4x + 3 = 0 C. 7x + 8x = 13 D. 0.04x - 0.08x = 0.40

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Recall that a linear equation in one variable x is an equation where the highest power of x is 1. This means the equation can be written in the form $ax + b = 0$, where $a$ and $b$ are constants.

Examine option A: $5x + 7 (x - 1) = -3x$. First, expand the parentheses: $5x + 7x - 7 = -3x$. Then combine like terms to check if the equation is linear.

Look at option B: $9x^{2} - 4x + 3 = 0$. Notice the term \$9x^{2}$, which has $x$ raised to the power of 2. This indicates the equation is quadratic, not linear.

Check option C: $7x + 8x = 13$. Combine like terms to get $15x = 13$, which is a linear equation since the highest power of $x$ is 1.

Review option D: $0.04x - 0.08x = 0.40$. Combine like terms to get $-0.04x = 0.40$, which is linear as well.

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주요 개념

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Definition of a Linear Equation

A linear equation is an algebraic equation in which each term is either a constant or the product of a constant and a single variable raised to the first power. It forms a straight line when graphed and does not include variables with exponents other than one.

Identifying Non-Linear Terms

Non-linear terms include variables raised to powers other than one, such as squares or higher exponents, or variables multiplied together. Recognizing these terms helps distinguish linear equations from quadratic or other polynomial equations.

Simplifying and Comparing Equations

Simplifying each equation by expanding and combining like terms allows for easier identification of the equation's degree. This process helps determine whether the equation is linear or not by revealing the highest power of the variable.