Question

how many solutions does this equation have?
-10u = -2(5u - 12) + 16
no solution
one solution
infinitely many solutions

Explanation:

Step1: Expand the right - hand side

First, we use the distributive property \(a(b - c)=ab - ac\) to expand \(-2(5u - 12)\). So \(-2(5u-12)=-2\times5u-2\times(- 12)=-10u + 24\). Then the equation \(-10u=-2(5u - 12)+16\) becomes \(-10u=-10u + 24+16\).

Step2: Simplify the right - hand side

We simplify the right - hand side by adding \(24\) and \(16\). So \(24 + 16=40\), and the equation is \(-10u=-10u + 40\).

Step3: Add \(10u\) to both sides

We add \(10u\) to both sides of the equation. \(-10u+10u=-10u + 40+10u\). The left - hand side \(-10u + 10u = 0\), and the right - hand side \(-10u+10u + 40=40\). So we get \(0 = 40\), which is a false statement.

Answer:

no solution