Question

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

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ANSWERED
asked 2020-12-25
To determine: The linear equation \(\displaystyle{1.2}{m}-{3.2}-{1.6}\) and check the solution.

Answers (1)

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.
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