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

Decimals
ANSWERED To solve: The linear equation
$$\displaystyle{0.65}{x}+{0.3}{x}={x}-{3}$$ 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.