Question

identify the equation as a conditional equation, a contradiction, or an identity. then give the solution set.
$6x - 8 = 3(7x - 2) + 7 - 15x$
part 1 of 2
the equation is
a conditional equation.
a contradiction.
an identity.
part 2 of 2
the solution set is
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Explanation:

Part 1 of 2

Step 1: Simplify the right - hand side

First, we expand and simplify the right - hand side of the equation \(6x - 8=3(7x - 2)+7 - 15x\).
Using the distributive property \(a(b + c)=ab+ac\), we have \(3(7x - 2)=3\times7x-3\times2 = 21x-6\).
So the right - hand side becomes \(21x-6 + 7-15x\).
Combine like terms: \(21x-15x=6x\) and \(-6 + 7 = 1\). So the right - hand side simplifies to \(6x + 1\).

Step 2: Compare both sides

The left - hand side of the equation is \(6x-8\) and the right - hand side is \(6x + 1\).
We set up the equation \(6x-8=6x + 1\). Subtract \(6x\) from both sides: \((6x-8)-6x=(6x + 1)-6x\).
This gives \(-8 = 1\), which is a false statement.

If an equation simplifies to a false statement (a statement that is never true, regardless of the value of the variable), then the equation is a contradiction.

Since the equation \(6x-8 = 3(7x - 2)+7-15x\) simplifies to a false statement (\(-8=1\)), there are no values of \(x\) that will make the equation true. The solution set of a contradiction is the empty set.

Answer:

a contradiction.

Part 2 of 2