Question

To solve: The linear equation 0.65x+0.3x=x-3

Decimals
ANSWERED
asked 2021-08-17
To solve: The linear equation
\(\displaystyle{0.65}{x}+{0.3}{x}={x}-{3}\)

Expert Answers (1)

2021-08-18
Step 1
Consider the linear equation.
\(\displaystyle{0.65}{x}+{0.3}{x}={x}-{3}\)
Subtract x from both sides of the equation.
\(\displaystyle{0.65}{x}+{0.3}{x}-{x}={x}-{3}-{x}\)
Combine the like terms.
\(\displaystyle{\left({0.65}{x}-{0.3}{x}-{x}\right)}={\left({x}-{x}\right)}-{3}\)
\(\displaystyle{0.05}{x}={0}-{3}\)
\(\displaystyle{0.05}{x}=-{3}\)
Express the decimal linear equation as an equivalent linear equation without decimals.
Multiply both sides of the equation by 100.
\(\displaystyle{100}{\left({0.05}{x}\right)}={100}{\left(-{3}\right)}\)
\(\displaystyle{5}{x}=-{300}\)
Divide both sides of the equation by 5
\(\displaystyle{\frac{{{5}{x}}}{{{5}}}}={\frac{{{300}}}{{{5}}}}\)
\(\displaystyle{x}={60}\)
Check the solution by substituting \(\displaystyle{x}={60}\) in the original equation.
\(\displaystyle{0.65}{\left({60}\right)}+{0.3}{\left({60}\right)}=^{{?}}{\left({60}\right)}-{3}\)
\(\displaystyle{39}+{18}=^{{?}}{60}-{3}\)
\(\displaystyle{57}={57}\) True
Since \(\displaystyle{x}={60}\) satisfies the original equation, the solution is 60.
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