Questions: Ex 3: Identify each equation as a conditional equation, a contradiction, or an identity. a) 6x-3=2(3x-2) b) 6x-3=2(3x-2)+1

Transcript text: Ex 3: Identify each equation as a conditional equation, a contradiction, or an identity. a) $6 x-3=2(3 x-2)$ b) $6 x-3=2(3 x-2)+1$

Solution

Solution Steps

To determine whether each equation is a conditional equation, a contradiction, or an identity, we need to simplify both sides of the equation and compare the results.

Simplify both sides of the equation.
Compare the simplified forms:
- If the simplified forms are identical, the equation is an identity.
- If the simplified forms result in a false statement (e.g., $0 = 1$), the equation is a contradiction.
- Otherwise, the equation is conditional.

Step 1: Simplify the Equation (a)

Given equation: \[ 6x - 3 = 2(3x - 2) \]

First, distribute the 2 on the right-hand side: \[ 6x - 3 = 6x - 4 \]

Step 2: Compare Both Sides of the Equation (a)

Subtract $6x$ from both sides: \[ 6x - 3 - 6x = 6x - 4 - 6x \] \[ -3 = -4 \]

This is a contradiction because $-3$ does not equal $-4$.