Question

tell whether each equation has one solution, no solution, or an infinite number of solutions. 3(4 - \frac{1}{3}x)=-2x - 10 + x. answer: no solution one solution infinitely many solutions

Explanation:

Step1: Expand the left - hand side

$3(4-\frac{1}{3}x)=3\times4 - 3\times\frac{1}{3}x=12 - x$

Step2: Simplify the right - hand side

$-2x-10 + x=-x - 10$

Step3: Set up the equation

$12 - x=-x - 10$

Step4: Add \(x\) to both sides

$12 - x+x=-x - 10+x$
$12=-10$ (False statement)

Answer:

no solution