Question

given the unfinished equation, $4x - 3 =$ ?, which expression below will make the equation true for all values of $x$?

a $4x - 3$

b $3x$

c $3x - 3$

Explanation:

Step1: Analyze the requirement

We need an expression that is equal to \(4x - 3\) for all values of \(x\). This means the left - hand side (\(4x - 3\)) and the right - hand side (the expression we choose) must be identical expressions.

Step2: Evaluate Option A

Option A is \(4x-3\). If we set the equation as \(4x - 3=4x - 3\), for any value of \(x\), when we subtract \(4x\) from both sides, we get \(- 3=-3\), which is always true.

Step3: Evaluate Option B

Option B is \(3x\). Let's set up the equation \(4x - 3 = 3x\). Subtract \(3x\) from both sides: \(x-3 = 0\), so \(x = 3\). This equation is only true when \(x = 3\), not for all values of \(x\).

Step4: Evaluate Option C

Option C is \(3x-3\). Set up the equation \(4x - 3=3x - 3\). Subtract \(3x\) from both sides: \(x-3=-3\), then add 3 to both sides: \(x = 0\). This equation is only true when \(x = 0\), not for all values of \(x\).

Answer:

A. \(4x - 3\)