Question

10
tell whether the equation has one solution, no solution, or an infinite number of solutions.
2.8 + 0.1x = 0.3(2 - x)
answer:
no solution
one solution
infinitely many
solutions

Explanation:

Step1: Expand the right-hand side

$2.8 + 0.1x = 0.6 - 0.3x$

Step2: Collect x terms on left

$2.8 + 0.1x + 0.3x = 0.6$
$2.8 + 0.4x = 0.6$

Step3: Isolate the x term

$0.4x = 0.6 - 2.8$
$0.4x = -2.2$

Step4: Solve for x

$x = \frac{-2.2}{0.4} = -5.5$

Answer:

one solution