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Solve the equation for x

Solve the equation for x-example-1

1 Answer

4 votes

Answer:


\large\boxed{\tt x=-1}

Explanation:


\textsf{We are asked to solve the equation for x. We are given 2 expressions with }


\textsf{This means that we are asked for the \underline{Absolute Value} of the expressions, or mainly}


\textsf{the equation.}


\large\underline{\textsf{What is Absolute Value?}}


\textsf{Absolute Value is a term that is greater than 0, which represents the positive}


\textsf{distance from 0. Say you were asked to find the Absolute Value of -3, it would}


\textsf{be 3 since the distance away from 0 is still 3.}


\large\underline{\textsf{Find the Absolute Value of our Equation;}}


\tt | 3x+5| = |2x-4|


\textsf{The Absolute Value of 3x is still 3x.}


\textsf{The Absolute Value of 5 is still 5.}


\textsf{The Absolute Value of 2x is still 2x.}


\textsf{The Absolute Value of -4 is 4.}


\underline{\textsf{We should have;}}


\tt 3x+5 = 2x+4


\textsf{We may begin solving for x by using the \underline{Properties of Equality}.}


\large\underline{\textsf{What are the Properties of Equality?}}


\textsf{The Properties of Equality are Properties that allow us to manipulate equations.}


\textsf{There are 9 properties of equality that we can use, each allowing us to simplify}


\textsf{one side of an equation. These properties are mainly used to find missing variables.}


\textsf{Let's solve for x by using the Properties of Equality.}


\large\underline{\textsf{Solving for x;}}


\tt 3x+5 = 2x+4


\textsf{Our goal is to have x only on one side of the equation, and constants only on one}


\textsf{side of the equation as well. We will need the Subtraction Property of Equality}


\textsf{which states that if 2 same numbers are subtracted from both sides of the}


\textsf{equation, then both expressions still equal each other.}


\underline{\textsf{Use the Subtraction Property of Equality;}}


\textsf{Use this property to subtract 2x from both sides of the equation.}


\tt 3x-2x+5 = 2x-2x+4


\tt x+5 =4


\textsf{Use this property again to subtract 5 from both sides of the equation.}


\tt x+5-5 =4-5


\large\boxed{\tt x=-1}

User James Addison
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