Question # To determine: The linear equation displaystyle{1.2}{m}-{3.2}-{1.6} and check the solution.

Decimals
ANSWERED To determine: The linear equation $$\displaystyle{1.2}{m}-{3.2}-{1.6}$$ and check the solution. 2020-12-26
Subtract 0.8 m from both sides of the equation.
$$\displaystyle{1.2}{m}-{3.2}-{0.8}{m}={0.8}{m}-{1.6}-{0.8}{m}$$
Combine the like terms.
$$\displaystyle{\left({1.2}{m}-{0.8}{m}\right)}-{3.2}={\left({0.8}{m}-{0.8}{m}\right)}-{1.6}$$
$$\displaystyle{0.4}{m}-{3.2}={0}-{1.6}$$
$$\displaystyle{0.4}{m}-{3.2}=-{1.6}$$
Again, add 3.2 to both sides of the equation.
$$\displaystyle{0.4}{m}-{3.2}+{3.2}=-{1.6}+{3.2}$$
Combine the like terms.
$$\displaystyle{0.4}{m}-{0}=-{1.6}+{3.2}$$
$$0.4\ m = 1.6$$
Express rhe decimal linear equation as an equivalent linear equation without decimals.
Multiply both sides of the equation by 10.
$$\displaystyle{10}{\left({0.4}{m}\right)}={10}{\left({1.6}\right)}$$
$$4\ m = 16$$
Divide both sides of the equation by 4.
$$\displaystyle\frac{{{4}{m}}}{{4}}=\frac{16}{{4}}$$
$$m = 4$$
Check the solution by substituting $$m = 4$$ in the original equation.
$$\displaystyle{1.2}{\left({4}\right)}-{3.2}{o}{v}{e}{r}{s}{e}{t}{\left(?\right)}{\left(=\right)}{0.8}{\left({4}\right)}-{1.6}$$
$$\displaystyle{4.8}-{3.2}{o}{v}{e}{r}{s}{e}{t}{\left(?\right)}{\left(=\right)}{3.2}-{1.6}v$$
$$1.6 = 1.6$$
Since $$m = 4$$ satisfiesnthe original equation, the solution is 4.