Question

how many solutions does this equation have? 7(2w + 1) = 14w + 1 no solution one solution two solutions infinitely many solutions

Explanation:

Step1: Expand the left side

We use the distributive property \(a(b + c)=ab+ac\) to expand \(7(2w + 1)\). So \(7\times2w+7\times1 = 14w + 7\). The equation becomes \(14w+7=14w + 1\).

Step2: Subtract \(14w\) from both sides

Subtract \(14w\) from each side of the equation \(14w + 7=14w+1\). We get \((14w - 14w)+7=(14w - 14w)+1\), which simplifies to \(7 = 1\).
Since \(7=1\) is a false statement, there are no values of \(w\) that will satisfy the original equation.

Answer:

no solution