Question

Determine whether each equation is an identity, a conditional equation, or a contradiction. Give the solution set. -0.6(x-5)+0.8(x-6) = 0.2x - 1.8

Accepted Answer

First, distribute the constants on the left side of the equation to remove the parentheses: apply the distributive property to both terms, so calculate $$-0.6(x - 5)$$ and $$0.8(x - 6)$$ separately. After distributing, combine like terms on the left side to simplify the expression into the form $$ax + b. $$Rewrite the equation with the simplified left side and the right side as given: $$ax + b = 0.2x - 1.8. $$Next, get all variable terms on one side and constant terms on the other side by subtracting $$0.2x$$ from both sides and adding or subtracting constants accordingly. Finally, analyze the resulting equation: if the variable terms cancel out and you get a true statement (like $$c = c$$), it's an identity; if you get a false statement (like $$c = d$$ where $$c 
eq d$$), it's a contradiction; otherwise, solve for $$x to $$find the solution set for a conditional equation.

Determine whether each equation is an identity, a conditional equation, or a contradiction. Give the solution set. -0.6(x-5)+0.8(x-6) = 0.2x - 1.8

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Key Concepts

Types of Equations: Identity, Conditional, and Contradiction

Solving Linear Equations

Solution Set of an Equation