Question

solve the equation below. whats the value of n? there are many ways you could solve this equation. one way you can start is by rewriting this equation without a fraction. what move can you make to get rid of the fraction on the left while keeping the equation balanced? \\(\frac{3}{2}(7 + 3n) = 3 + 3n\\) multiply both sides of the equation by 3 divide both sides of the equation by 2 multiply both sides of the equation by 2

Explanation:

To eliminate the fraction \(\frac{3}{2}\) in the equation \(\frac{3}{2}(7 + 3n)=3 + 3n\), we use the multiplication property of equality. The denominator of the fraction is 2, so multiplying both sides by 2 will cancel the denominator. Let's check:

• If we multiply both sides by 3: The fraction \(\frac{3}{2}\) would become \(\frac{9}{2}\), not eliminating the fraction.
• If we divide both sides by 2: The left side would be \(\frac{3}{4}(7 + 3n)\), introducing a new fraction.
• If we multiply both sides by 2: The left side becomes \(3(7 + 3n)\) (since \(2\times\frac{3}{2}=3\)) and the right side becomes \(2(3 + 3n)\), eliminating the fraction.

Answer:

Multiply both sides of the equation by 2