Question

identify the number of solutions to the linear equation given below. 0.25x + \frac{2}{5}x = 0.5x - \frac{9}{30} answer: no solution one solution infinitely many solutions

Explanation:

Step1: Convert to decimals

$\frac{2}{5}=0.4$, $\frac{9}{30}=0.3$
Equation becomes: $0.25x + 0.4x = 0.5x - 0.3$

Step2: Combine like terms (left)

$0.25x + 0.4x = 0.65x$
Equation: $0.65x = 0.5x - 0.3$

Step3: Isolate x terms

$0.65x - 0.5x = -0.3$
$0.15x = -0.3$

Step4: Solve for x

$x = \frac{-0.3}{0.15} = -2$

Answer:

one solution