Final answer:
The values of x that satisfy the inequalities x-4<3 and 3x > -6 are in the range -2 < x < 7. The most familiar inequality sign is the “not equal sign (≠)”. But to compare the values on the inequalities, the following symbols are used.
Step-by-step explanation:
The student is asking to find the range of values for x that satisfy both inequalities x-4<3 and 3x > -6. To solve the first inequality, add 4 to both sides to get x < 7. For the second inequality, divide both sides by 3 to find x > -2. The range of values for x that satisfies both inequalities is when x is greater than -2 and less than 7. Therefore, the solution can be written as -2 < x < 7.
In Algebra, inequality is a mathematical statement that shows the relation between two expressions using the inequality symbol. The expressions on both sides of an inequality sign are not equal. It means that the expression on the left-hand side should be greater than or less than the expression on the right-hand side or vice versa. If the relationship between two algebraic expressions is defined using the inequality symbols, then it is called literal inequalities.
Definition: “If two real numbers or the algebraic expressions are related by the symbols “>”, “<”, “≥”, “≤”, then the relation is called an inequality.”
For example, x>3 (x should be greater than 3)
Open Sentence: The inequality is said to be an open sentence if it has only one variable.