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

Question

Determine whether each equation is an identity, a conditional equation, or a contradiction. Give the solution set. See Example 4.4(x + 7) = 2(x + 12) + 2(x + 1)

Accepted Answer

Hello, everyone. We are asked to classify the equation as a contradiction, an identity or a conditional and then provide its solution set. The equation we are given is nine multiplied by the parentheses. X plus five equals three, multiplied by the parentheses. X plus 11 plus six multiplied by the parentheses. X plus eight. Our answer choices are a conditional and the set is 45 B conditional with a set of zero C contradiction with the null set D identity with a set of all real numbers. So I'm gonna rewrite this equation with all of its parentheses. So nine multiplied by, in parentheses, X plus five equals three multiplied by, in parentheses, X plus 11 plus six multiplied by the parentheses X plus eight. My first step in finding out if it's a contradiction identity or conditional is to try to solve it in order to solve it. I'm gonna first use the distributive property and multiply everything outside parentheses into them. So nine multiplied by X is nine, X nine, multiplied by five is positive 45. That's gonna equal three multiplied by X which is three, X and three multiplied by 11 which is positive 33 and then six multiplied by X is positive six X six multiplied by a positive eight is positive 48. OK. Next step, combining my like terms nine X plus will not change, that will stay the same on the left hand side, on my right hand side, I'm combining three X and six X to get nine X and then I need to combine 33 and which is 81. Next, I'm going to move my variables to the left by subtracting nine X from both sides. And when I do that, they cancel out, so I have no variable left. So this means I either have a contradiction or an identity. But let's look at what's left over right now. I have that 45 equals 81. 45 does not equal 81. So this is a contradiction and our solution set is the null set or the empty set. So this is answer choice. C it's a contradiction because no matter what value I plug in 45 will not equal 81. Have a nice day.

Determine whether each equation is an identity, a conditional equation, or a contradiction. Give the solution set. See Example 4.4(x + 7) = 2(x + 12) + 2(x + 1)

Key Concepts

Identities

Conditional Equations

Contradictions

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