Determine whether each equation is an identity, a conditional ...

Question

Determine whether each equation is an identity, a conditional equation, or a contradiction. Give the solution set. See Example 4. 2(x - 8) = 3x - 16

Accepted Answer

Hello, everyone. We are asked to classify the equation as a contradiction, an identity or a conditional, then provide the solution set. The equation we are given is 12, multiplied by open parentheses. X minus six, closed parentheses equals 13, X minus 72. Our answer choices are a conditional with a solution set of zero B contradiction with a null set C identity. And the solution set is all real numbers D conditional with a solution set of negative one. So we're gonna start by rewriting this equation. So 12 multiplied by the parentheses X minus six equals 13, X minus 72. So my first step, I'm going to distribute 12 into the parentheses. So 12 multiplied by X is 12, X, 12, multiplied by negative six is negative 72. And this will equal 13 X minus 72. Next, I'm gonna move my variable. So I'm gonna move that whole term by doing the opposite operation. I'm gonna subtract 13 X from both sides. I just like having my variables on the left hand side. If I can, this will give us negative one, X minus 72 equals negative 72. Moving the constants. I'm gonna add 72 to both sides. And when I do, I end up with negative one, X equals zero. I'm still gonna divide both sides by negative one but zero divided by anything is zero. So here X equals zero, this doesn't mean we have no solution. It means that our solution set is zero. So this is a conditional because this equation will be true where X equals zero. So that's answer choice. A have a nice day.

Determine whether each equation is an identity, a conditional equation, or a contradiction. Give the solution set. See Example 4. 2(x - 8) = 3x - 16

Key Concepts

Types of Equations: Identity, Conditional, and Contradiction

Solving Linear Equations

Checking Solutions and Solution Sets

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