Question

how many solutions does this equation have? solve on paper and enter your answer on zearn. $9x = \frac{1}{5}(45x + 5)$ no solutions one solution infinitely many solutions

Explanation:

Step1: Simplify the right - hand side

We use the distributive property \(a(b + c)=ab+ac\). For \(\frac{1}{5}(45x + 5)\), we have \(\frac{1}{5}\times45x+\frac{1}{5}\times5 = 9x + 1\). So the equation becomes \(9x=9x + 1\).

Step2: Subtract \(9x\) from both sides

Subtract \(9x\) from both sides of the equation \(9x=9x + 1\). We get \(9x-9x=9x + 1-9x\), which simplifies to \(0 = 1\).

Since the statement \(0 = 1\) is false, the equation has no solutions.

Answer:

No solutions