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.

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.