Question

determine whether each equation is an identity, a conditional equation, or a contradiction. give the solution set
$5x - 3 = 2(2x + 2) - 1$
is the equation a conditional equation, an identity, or a contradiction?
a. identity
b. conditional equation
c. contradiction

Explanation:

Step1: Simplify the right side

First, expand the right - hand side of the equation \(5x - 3=2(2x + 2)-1\). Using the distributive property \(a(b + c)=ab+ac\), we have \(2(2x + 2)=4x + 4\). So the equation becomes \(5x-3 = 4x + 4-1\).

Step2: Simplify the right side further

Simplify \(4x + 4-1\) to get \(4x+3\). Now our equation is \(5x - 3=4x + 3\).

Step3: Solve for x

Subtract \(4x\) from both sides: \(5x-4x-3=4x - 4x+3\), which simplifies to \(x - 3=3\). Then add 3 to both sides: \(x-3 + 3=3 + 3\), so \(x = 6\).

Since the equation is true only for \(x = 6\) (not for all real numbers, and it's not a contradiction as there is a solution), it is a conditional equation.

Answer:

B. conditional equation