Question

# The solution of the inequality and interval notation.Given:displaystyle{10}+{x}<{6}{x}-{10}

Decimals

The solution of the inequality and interval notation.
Given:
$$\displaystyle{10}+{x}<{6}{x}-{10}$$

2020-12-25

Concept used:
Consider the following steps to solve one variable linear inequality:
If an equation contains fractions or decimals, multiply both sides by the LCD to clear the equation of fractions or decimals.
Use the distributive property to remove parentheses if they are present.
Simplify each side of the inequality by combining like terms.
Get all variable terms on one side and all numbers on the other side by using the addition property of inequality.
Get the variable alone by using the multiplication property of equality.
The given inequality equation is,
$$\displaystyle{10}+{x}<{6}{x}-{10}$$
$$\displaystyle{10}+{x}-{6}{x}<{6}{x}-{10}-{6}{x}$$
$$\displaystyle{10}-{5}{x}<-{10}$$
$$\displaystyle{10}-{5}{x}-{10}<-{10}-{10}$$
Simplify further,
$$\displaystyle-{5}{x}<-{20}$$
$$\displaystyle\frac{{-{5}{x}}}{{5}}>\frac{{-{20}}}{ -{{5}}}$$
$$\displaystyle{x}>{4}$$
The interval notation of the inequality is written as $$\displaystyle{\left({4},\infty\right)}.$$
Hence, the solution of the inequality is $$\displaystyle{x}>{4}$$
and the interval notation is $$\displaystyle{\left({4},\infty\right)}.$$