Question

Is $v=-\frac{1}{3}$ a solution of $9 v-2=3 v ?$

   Is $v=-\frac{1}{3}$ a solution of $9 v-2=3 v ?$

Elementary Algebra

Elementary Algebra

Lynn Marecek 1st Edition

Chapter 2, Problem 4

Instant Answer

Solved by Expert Palitha Reddy

07/12/2021

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Step 1: Write down the given equation: 9v - 2 = 3v Show more…

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Is $v=-\frac{1}{3}$ a solution of $9 v-2=3 v ?$

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Key Concepts

Substitution Method

The substitution method is a fundamental technique in algebra where a specific value is replaced for a variable in an equation to see if it fulfills the condition. This method is often applied to test the validity of a presumed solution, ensuring both sides of the equation balance when the value is substituted.

Linear Equations

Linear equations, typically of the form ax + b = cx + d, are equations where the variables are raised to the first power and do not have products between variables. Understanding the structure of linear equations, including how to simplify and isolate terms, helps in determining whether a candidate value satisfies the equation as intended.

Verification of a Solution

This concept involves checking whether a proposed value indeed satisfies the given equation by replacing the variable with the candidate value. In any equation, a solution is only valid if, after substitution, the left-hand side equals the right-hand side. This step is critical in confirming the accuracy of the result obtained either by guess or by solving.

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