The document discusses linear and literal equations and inequalities. It defines linear equations as equations with variables of exponent 1 that can be solved by isolating the variable. Literal equations contain two or more variables and specify which variable to solve for. Inequalities are solved like equations but the inequality symbol changes if multiplying or dividing by a negative number. Examples are provided for solving each type.

1. Linear and Literal Equations
Objectives
• Solve multi-step linear equations
• Solve literal equations for a given variable
• Solve linear inequalities

2. linear equationlinear equationlinear equationlinear equation – an equation with a variable of order 1 (i.e.,
any variables have an exponent of 1).
To solve a linear equation, isolate the variable on one side of
the equation.
Example:
Solve  5 7 2 1x x  Solve  5 7 2 1x x  

3. linear equationlinear equationlinear equationlinear equation – an equation with a variable of order 1 (i.e.,
any variables have an exponent of 1).
To solve a linear equation, isolate the variable on one side of
the equation.
Example:
Solve  5 7 2 1x x  Solve  5 7 2 1x x  
5 7 2 2x x  

4. linear equationlinear equationlinear equationlinear equation – an equation with a variable of order 1 (i.e.,
any variables have an exponent of 1).
To solve a linear equation, isolate the variable on one side of
the equation.
Example:
Solve  5 7 2 1x x  Solve  5 7 2 1x x  
5 7 2 2x x  
25 27 2 2xx xx  
3 7 2x  

5. linear equationlinear equationlinear equationlinear equation – an equation with a variable of order 1 (i.e.,
any variables have an exponent of 1).
To solve a linear equation, isolate the variable on one side of
the equation.
Example:
Solve  5 7 2 1x x  Solve  5 7 2 1x x  
5 7 2 2x x  
25 27 2 2xx xx  
3 7 2x  
73 77 2x    
3 9x 

6. linear equationlinear equationlinear equationlinear equation – an equation with a variable of order 1 (i.e.,
any variables have an exponent of 1).
To solve a linear equation, isolate the variable on one side of
the equation.
Example:
Solve  5 7 2 1x x  Solve  5 7 2 1x x  
5 7 2 2x x  
25 27 2 2xx xx  
3 7 2x  
73 77 2x    
3 9x 
3 9
3 3
x
3x 

7. literal equationliteral equationliteral equationliteral equation – an equation with two or more variables
Whenever you are asked to solve a literal equation, you will
generally be told for what variable you are solving. You will
then use inverse operations to isolate the desired variable.
Example: Solve for h.
2
bh
A 

8. literal equationliteral equationliteral equationliteral equation – an equation with two or more variables
Whenever you are asked to solve a literal equation, you will
generally be told for what variable you are solving. You will
then use inverse operations to isolate the desired variable.
Example: Solve for h.
2
bh
A 
2
2 2
bh
A
 
  
 
Undo dividing by multiplying
2A bh

9. literal equationliteral equationliteral equationliteral equation – an equation with two or more variables
Whenever you are asked to solve a literal equation, you will
generally be told for what variable you are solving. You will
then use inverse operations to isolate the desired variable.
Example: Solve for h.
2
bh
A 
2
2 2
bh
A
 
  
 
Undo dividing by multiplying
2A bh
2A
h
b


10. inequalityinequalityinequalityinequality – a relation of two unequal expressions
To solve an inequality, solve as you would an equation, not
losing the inequality symbol between the expressions. The
inequality symbol changes direction if you multiplymultiplymultiplymultiply or dividedividedividedivide
by a negative numbernegative numbernegative numbernegative number.
Examples: Solve Solve4 3 17x   3 4 5 10x x  Examples: Solve Solve4 3 17x   3 4 5 10x x  

11. inequalityinequalityinequalityinequality – a relation of two unequal expressions
To solve an inequality, solve as you would an equation, not
losing the inequality symbol between the expressions. The
inequality symbol changes direction if you multiplymultiplymultiplymultiply or dividedividedividedivide
by a negative numbernegative numbernegative numbernegative number.
Examples: Solve Solve4 3 17x   3 4 5 10x x  Examples: Solve Solve4 3 17x  
4 20x 
3 4 5 10x x  

12. inequalityinequalityinequalityinequality – a relation of two unequal expressions
To solve an inequality, solve as you would an equation, not
losing the inequality symbol between the expressions. The
inequality symbol changes direction if you multiplymultiplymultiplymultiply or dividedividedividedivide
by a negative numbernegative numbernegative numbernegative number.
Examples: Solve Solve4 3 17x   3 4 5 10x x  Examples: Solve Solve4 3 17x  
4 20x 
5x 
3 4 5 10x x  

13. inequalityinequalityinequalityinequality – a relation of two unequal expressions
To solve an inequality, solve as you would an equation, not
losing the inequality symbol between the expressions. The
inequality symbol changes direction if you multiplymultiplymultiplymultiply or dividedividedividedivide
by a negative numbernegative numbernegative numbernegative number.
Examples: Solve Solve4 3 17x   3 4 5 10x x  Examples: Solve Solve4 3 17x  
4 20x 
5x 
3 4 5 10x x  
2 14x  

14. inequalityinequalityinequalityinequality – a relation of two unequal expressions
To solve an inequality, solve as you would an equation, not
losing the inequality symbol between the expressions. The
inequality symbol changes direction if you multiplymultiplymultiplymultiply or dividedividedividedivide
by a negative numbernegative numbernegative numbernegative number.
Examples: Solve Solve4 3 17x   3 4 5 10x x  Examples: Solve Solve4 3 17x  
4 20x 
5x 
3 4 5 10x x  
2 14x  
7x 