identify the number of solutions to the linear equation given below. 0.25x + \\frac{2}{5}x = 0.5x…

Explanation:

Step1: Convert decimals to fractions

$0.25=\frac{1}{4}$, so the equation becomes $\frac{1}{4}x+\frac{2}{5}x = 0.5x-\frac{9}{30}$. And $0.5=\frac{1}{2}$, then $\frac{1}{4}x+\frac{2}{5}x=\frac{1}{2}x - \frac{3}{10}$.

Step2: Find a common - denominator

The common denominator of 4, 5 and 2 is 20. Rewrite the left - hand side: $\frac{1\times5}{4\times5}x+\frac{2\times4}{5\times4}x=\frac{5}{20}x+\frac{8}{20}x=\frac{5 + 8}{20}x=\frac{13}{20}x$. Rewrite the right - hand side: $\frac{1\times10}{2\times10}x-\frac{3}{10}=\frac{10}{20}x-\frac{6}{20}$.

Step3: Simplify the equation

The equation $\frac{13}{20}x=\frac{10}{20}x-\frac{6}{20}$ can be rewritten as $\frac{13}{20}x-\frac{10}{20}x=-\frac{6}{20}$.

Step4: Combine like terms

$\frac{13x - 10x}{20}=-\frac{6}{20}$, which simplifies to $\frac{3}{20}x=-\frac{6}{20}$.

Step5: Solve for x

Multiply both sides by $\frac{20}{3}$, we get $x = - 2$.

Answer:

one solution