EdReady: Solving Equations and Inequalities

Solving Equations and Inequalities with Properties of Equality, Solving Multi-Step Equations, Special Cases and Applications, Formulas, Solving One-Step Inequalities, Multi-Step Inequalities, Compound Inequalities, Equations and Inequalities and Absolute Value

linear equation

ax + b = c; x is a variable

like terms

terms with the same variable raised to the same power

Identity Property of Zero/Additive Identity

adding 0 does not change the value

Multiplicative Identity

multiplying by 1 does not change the reciprocal

How to solve multi-step equations

Simplify: Combine like terms

Put all variables onto one side

Isolate the variable with inverse operations

Check with substitutions

How to solve word problems

Identify what to find

Determine constants (known values) and variables (unknowns)

Write the equation with the constants and variables (translate)

Solve the equation and check the answer

Write a sentence that answers the question

When the variable disappears

True or false statement:

if True: all real numbers

if False: no solution

distance formula

d = rt

Celsius to Fahernheit

F = 9/5C + 32

Fahrenheit to Celsius

C = 59(F-32)

inequalities

shows a relationship between two expressions

closed/shaded circle

less/greater than or equal to

open circle

less/greater than

Addition and Subtraction Properties of Inequality

if a > b, then a + c > b + c

if a > b, then a - c > b - c

When multiplying/dividing inequalities by negative numbers

flip the inequality sign

Multiplication and Division Properties of Inequality

if a > b, then ac > bc, if c > 0

if a > b, then ac < bc, if c < 0

if a > b, then a/c > b/c, if c > 0

if a > b,then a/c < b/c, if c < 0

compound inequality

two inequality statements linked by AND or OR

AND statement

split into two statements

solution of an AND statement

intersection of solutions (overlap); solution is the inequality that overlaps

How to solve AND statements (x < a AND a < y; x < a < y)

solve and combine or solve as is

OR statement (x < y or y > x)

values that make either equation true

How to solve OR statements

solve each inequality separately

Inequality solutions can

have no solutions or be the set of all real numbers

Absolute value equation solutions: |x| = a

x = a or x = -a

How to solve absolute value equations

Write the equation twice: one with a positive answer (a) and one with a negative answer (-a)

Solve both equations: x = a or x = -a

Absolute value inequalities: less than (or equal to)

AND statement: |x| < a = -a < x < a

Absolute value inequalities: greater than (or equal to)

OR statement: |x| > a = x < -a or x > a

How to solve |x| < a inequalities

Simplify to |x| < a format

Set to -a < x < a (a is the answer) and solve

How to solve |x| > a inequalities

Set to x < -a or x > a format (switch inequality for opposite)

Solve for both

Absolute value equations with initial negative answers

no solution (absolute value cannot be negative)