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Is this a linear inequalities 3x + 5 < 9?

User Arany
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1 Answer

3 votes

Answer:

yes

Explanation:

You want to know if 3x+5 < 9 is a linear inequality.

Inequality

The relation is an inequality because a comparison symbol other than an equal sign is used.

Linear

The relation is linear because the variable expression is of degree 1.

The relation 3x+5 < 9 is a linear inequality.

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Additional comment

The parts of the expression are ...

  • 3x — a "term" consisting of the product of a coefficient (3) and a variable (x). The implied exponent of x is 1. That is its degree.
  • + — a math operator indicating addition
  • 5 — a "term" consisting of a constant (5). This can also be referred to as a coefficient.
  • < — a math relational operator telling you the expression on the left has a value less than that of the expression on the right. The presence of this symbol is what makes it an "inequality". Other relational operators are >, ≤, ≥, =, ≠. These may be represented differently in the context of a spreadsheet or computer program, where you might see != or <> for "not equal", for example.
  • 9 — another constant.

An expression consisting of one term can be called a "monomial." With 2 terms, it is a "binomial". With no particular number of terms, it is a "polynomial." In general a polynomial is a sum of terms of non-negative integer degree. (A constant has degree 0.)

If a term has more than one variable, its degree is the sum of the exponents of the variables. For example, 8xy³ has variable exponents 1 and 3, so its degree is 1+3 = 4.

The terms "linear", "quadratic", "cubic", and "quartic" are used to refer to polynomial expressions or terms of degrees 1, 2, 3, and 4, respectively. A first degree polynomial is a linear polynomial. Its graph is a straight line.

User Waymond
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