Recall that a function of the form f(x) = ax + b, a, b ∈ R are constants, is called a linear function, because its graph is a straight line.

**Linear Inequalities**

Recall that a function
of the form *f*(*x*) = *ax* + *b*, *a, b* *∈* R are constants, is called a linear function,
because its graph is a straight line. Here *a* is the slope of the
line and *b* is the *y*-intercept. If *a* ¹ 0, then *x*-intercept *x* = *-b/a* is obtained by solving *f*(*x*) = *ax* + *b* = 0*.*

But there are
situations where we need to consider linear inequalities.

For example to
describe a statement like “ *A tower is
not taller than fifty feet.*”

If *x* denotes the height of the tower in feet, then the above
statement can be expressed as *x* *≤* 50.

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