Question
Question: How do you solve the inequality \[3x+8>2\]?...
How do you solve the inequality 3x+8>2?
Solution
To solve this linear inequality in one variable, we have to take the variable terms to one side of the inequality, and the constant terms to the other side. Inequalities do not provide a fixed value as a solution; it gives a range. All the values in this range hold the inequality. To solve an inequality, we should know some of the properties of the inequality as follows, given thata>b. We can state the following from this.
a+k>b+k,k∈Real numbers
ak>bk,k∈Positive real numbers
ak<bk,k∈ Negative real numbers
Complete step by step solution:
We are asked to solve the inequality 3x+8>2. We will use the properties of inequalities to solve this question. The properties we will use are as follows, given thata>b. We can state the following from this.
a+k>b+k,k∈Real numbers
ak>bk,k∈Positive real numbers
By adding or subtracting a number to both sides of an inequality the sign of inequality does not change. Subtracting 8 from both sides of the inequality, we get