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Is the equation an identity or a contradiction? Give the solution set. \[ 6(x+1)+6=4 x+2 x+12 \] Part: \( \mathbf{0} / \mathbf{2} \) Part 1 of 2 The equation is an identity. The equation is a contradiction.

Ask by Ortiz Wright. in the United States
Feb 21,2025

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The equation is an identity, and the solution set is all real numbers.

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To determine whether the equation is an identity or a contradiction, we can simplify both sides. Starting with the left side: \[ 6(x+1)+6 = 6x + 6 + 6 = 6x + 12. \] Now, for the right side: \[ 4x + 2x + 12 = 6x + 12. \] Since both sides simplify to \( 6x + 12 \), the equation holds true for all values of \( x \), making it an identity. To summarize further, any equation that is always true regardless of the value of the variable is categorized as an identity. This means for our equation, \( 6(x+1)+6=4 x+2 x+12 \), you can plug in any real number for \( x \), and both sides will always be equal, which is a delightful property of identities in mathematics!

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