Question

solve the equation.
2(x - 3) - 4 = 0
select the correct choice below and, if necessary, fill in the answer box to complete your choice.
a. the solution is x = . (type an integer or a fraction.)
b. the solution is all real numbers.
c. there is no solution.

Explanation:

Step1: Expand the left side

Using the distributive property \(a(b - c)=ab - ac\), we expand \(2(x - 3)\) to get \(2x-6\). So the equation becomes \(2x - 6-4 = 0\).

Step2: Combine like terms

Combine the constant terms \(-6\) and \(-4\). So \(2x-(6 + 4)=0\), which simplifies to \(2x-10 = 0\).

Step3: Isolate the variable term

Add \(10\) to both sides of the equation. We get \(2x-10 + 10=0 + 10\), so \(2x=10\).

Step4: Solve for x

Divide both sides of the equation by \(2\). \(\frac{2x}{2}=\frac{10}{2}\), which gives \(x = 5\).

Answer:

A. The solution is \(x=\boldsymbol{5}\).