Question

how many solutions does this equation have?
d + 4(-5d - 8) = -14 - 19d
no solution
one solution
infinitely many solutions

Explanation:

Step1: Expand the left side

Using the distributive property \(a(b + c)=ab+ac\), we expand \(4(-5d - 8)\) as \(4\times(-5d)+4\times(-8)=-20d - 32\). So the left side of the equation becomes \(d-20d - 32=-19d - 32\). The equation is now \(-19d - 32=-14 - 19d\).

Step2: Simplify the equation

Add \(19d\) to both sides of the equation: \(-19d+19d - 32=-14 - 19d+19d\). This simplifies to \(-32=-14\).

Answer:

no solution