Definition: Any algebtraic expression whose degree is one is a linear expression.
A linear equation in one variable x is of the form:
in general y(x) = ax +b, where a is b are real.
Equations in 2 variables say x and y:
y=mx+c , slope and intercept form , m and c are any number, and
ax+by+c=0 a standard form,
are all linear equations in two variables x, and y.
Note: x^2+y^2 = 9 or xy+x+y =k are not linear equations as the algebraic expression is of 2nd degree. The epression involving sqrtx or sqrty type of terms can not be linear expressions.
a1x1+a2x2+a3x3+...+an*xn = k, where the xi (for i=1,2,...n ar n suffixes)) are n variables ans ai is ant number.
Inequalities: Inequalities are the relations involving linear expressons. Infact equation is a special case of relation of inequality only.
ax+by+c < 0 or ax+by+c>0 are inequalities, wheres
ax+by+c=0 is an equality.
ax+b<0 or ax+b>0 are inequalities whereas
ax+b=0 is an equality.
a1x1+a2x2+a3x3+....+anxn < b or a1x1+a2+x2+a3x3+....+anxn>b are linear inequalities, whereas
a1x1+a2x2+a3x3+....+anxn = b is a linear equality or equation. ( Note that the highest degree of the exression is one).
Equation always just has equal "=" in the problem, however, inequailty has one of the notation( <, >, <or=, >or=)
Equation has one solution if it linear, or 2 solution if it quardic, or 3 solution if cube. it means equation has number of solution equal it's degree.
Inequailty has region of solution.
linear equations and inequalities have only first power terms, no squared terms, no cubed terms, no terms to any power other than one.
equations are equal to something while inequalities are not necessarily equal to a specific answer.
y=2x+3 is a linear equality. If you replaced the = sign with <,>, or greater/less than or equal to sign it would be an inequality