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From the following, identify a linear equalnis \( \begin{array}{ll}\text { A) } 2 x+5 & \text { B) } 2 x+5<11\end{array} \)

Ask by Hills Ortiz. in India
Feb 20,2025

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Answer

Neither option A nor option B is a linear equation.

Solution

To identify a linear equation from the given options, we need to understand the definitions of linear equations and inequalities. 1. **Linear Equation**: An equation that can be written in the form \( ax + b = 0 \), where \( a \) and \( b \) are constants, and \( x \) is the variable. 2. **Linear Inequality**: An inequality that can be written in the form \( ax + b < c \) or \( ax + b > c \), where \( a \), \( b \), and \( c \) are constants. Now, let's analyze the options provided: - **Option A**: \( 2x + 5 \) - This is not an equation because it does not have an equality sign (=). It is simply an expression. - **Option B**: \( 2x + 5 < 11 \) - This is a linear inequality because it has a less than sign (<) and can be rearranged to the form \( 2x + 5 - 11 < 0 \). Since we are looking for a linear equation, neither option A nor option B qualifies as a linear equation. However, if we had to choose the one that is closest to a linear form, it would be option A, but it is not an equation. Thus, there is no linear equation among the provided options.

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Beyond the Answer

A linear equation is an equation that involves variables raised only to the first power, typically in the form of \(y = mx + b\), where \(m\) is the slope and \(b\) is the y-intercept. In this case, the option "A) \(2x + 5\)" represents a linear expression, but it is not an equation unless it is set equal to something. Option "B) \(2x + 5 < 11\)" is an inequality, not a linear equation. To form a linear equation from option A, you could set it equal to a value, like so: \(2x + 5 = 0\). This would transform it into a proper linear equation, showcasing how easy it is to convert an expression into an equation!

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