Equations are expressions in which both sides of the equality sign are considered equal.
A linear equation, or a first-degree equation, is an equation with the variable x is linear if it takes the form [ax + b =c] where [a], [b], and [c] are real numbers, and where [a 
0].
A linear equation is also referred to as a first-degree equation because the highest power applied to the variable is one.
If the expression [ 3x = 2 ] is true, then x must equal a value that, when multiplied by 3 is equivalent to 2.
If both sides of [ 3x = 2 ] are divided by three, we can isolate x as in [ 3x/3 = 2/3 ] = [ x = 2/3 ].
If the expression [ 3x = 2 ] is true, then x is equivalent to two-thirds because three multiplied by two-thirds is equal to two.
Properties of Equations:
Addition Property of Equality - For all real numbers [a], [b], and [c], the equations [a = b] and [a + c = b + c] are equivalent.
Multiplication Property of Equality - For all real numbers [a], [b], and [c], where [c 0], [a = b] and [ac = bc] are equivalent.
Procedure for solving a linear equation with one variable:
[1]. Remove fractions through multiplication of both sides of the equation by a common denominator.
[2]. Simplify both sides of the equation. Use the distributive property when attempting to remove parentheses and combining variables.
[3]. Get all variables on one side of the equation using the addition property of equality.
[4]. Make the coefficient of the variable [1] using the multiplication property.
Consider the following equation:
In order to remove the fractions, we can multiply both sides by [12]. This yields [2(x + 11) + 3(3x - 7) = 144].
We can simplify this further as [2x + 22 + 9x - 21 = 144]. Again, simplifying yields [11x + 1 = 144].
This becomes [11x = 143] or [x = 143/11] so [x = 13].
Consider the equation [ax + 5z = 7 + bz].
If we are asked to solve this equation with respect to the variable [z], we are essentially being asked to isoltate [z] on one side of the equation.
We can being by subtracting [bz] from both sides, yielding [ax + 5z - bz = 7].
Then, we can move towards isolating the [z] variable by subtracting the [ax] from both sides, yielding [5z - bz = 7 - ax].
We can use the distributive property to create [z(5 - b) = 7 - ax].
We can divide both sides by [(5-b)], resulting in [z = (7 - ax) / (5 - b)] or, written more clearly:
