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 Depdendent Variable

 Number of equations to solve: 23456789
 Equ. #1:
 Equ. #2:

 Equ. #3:

 Equ. #4:

 Equ. #5:

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 Equ. #7:

 Equ. #8:

 Equ. #9:

 Solve for:

 Dependent Variable

 Number of inequalities to solve: 23456789
 Ineq. #1:
 Ineq. #2:

 Ineq. #3:

 Ineq. #4:

 Ineq. #5:

 Ineq. #6:

 Ineq. #7:

 Ineq. #8:

 Ineq. #9:

 Solve for:

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# SOLVING LINEAR EQUATIONS

Definition:

• A linear equation in one variable can be written in the form

ax + b = c

for real numbers a, b, and c, with a ≠ 0.

Important Properties:
If a, b, and c are real numbers, then

a = b and a + c = b + c

are equivalent equations. (That is, you can add or subtract the same quantity on both sides of the
equation without changing the solution.)

• Multiplication Property of Equality: If a, b, and c are real numbers and c ≠ 0, then

a = b and ac = bc

are equivalent equations. (That is, you can multiply or divide the same nonzero quantity on both
sides of the equation without changing the solution.)

Common Mistakes to Avoid:

• When clearing the parentheses in an expression like 7-(2x-4), remember that the minus sign acts
like a factor of -1. After using the distributive property, the sign of every term in the parentheses
will be changed to give 7 - 2x + 4.

• To clear fractions from an equation, multiply every term on each side by the lowest common de-
nominator. Remember that   is considered one term, whereas, is considered two
terms. To avoid a mistake, clear all parentheses using the distributive property before multiplying
every term by the common denominator.

• To preserve the solution to an equation, remember to perform the same operation on both sides of
the equation.

PROBLEMS

Solve for x in each of the following equations:

 No Solution

NOTE: Whenever the variable disappears
and a false statement (such as 72 = 0) re-
sults, the equation has no solution.

 All real numbers

NOTE: Whenever the variable disappears
and a true statement (such as 0 = 0) results,
the equation is an identity. An identity is
true regardless of the number substituted
into the variable. As a result, we write \all