Question

geometry support unit 1—introduction to geometry notes

1. given: ( 6x - 4 = 3x + 8 ).

prove: ( x = 4 )

Explanation:

Step1: Subtract \(3x\) from both sides

\(6x - 4-3x=3x + 8-3x\)
\(3x-4 = 8\) (Subtraction Property of Equality)

Step2: Add \(4\) to both sides

\(3x-4 + 4=8 + 4\)
\(3x=12\) (Addition Property of Equality)

Step3: Divide both sides by \(3\)

\(\frac{3x}{3}=\frac{12}{3}\)
\(x = 4\) (Division Property of Equality)

Answer:

Statement	Reason
\(6x-4-3x=3x + 8-3x\)	Subtraction Property of Equality
\(3x-4 = 8\)	Simplification
\(3x-4 + 4=8 + 4\)	Addition Property of Equality
\(3x=12\)	Simplification
\(\frac{3x}{3}=\frac{12}{3}\)	Division Property of Equality
\(x = 4\)	Simplification