Reviewing skills needed to succeed in Algebra 2.

Need a common denominator OR can multiply both sides of equation by common denominator to get rid of fractions Example: #10

Always switch the direction of the sign when multiplying or dividing by a negative number COMPOUND INEQUALTIES: AND/OR #21: -5 < -2h -15 < 7

Always set up 2 equations or inequalities before solving Always isolate the absolute value expression before setting up 2 equations or inequalities When solving absolute value inequalities, always switch the direction of the inequality sign when writing the ‘negative’ inequality When < or <, its and ‘AND’ compound inequality When > or >, it an ‘OR’ compound inequality

1.Solve 2|2x-5|= |3x -2|< 5 Answer: NO SOLUTION…tricky. An absolute value expression cannot equal a negative quantity.

Parallel lines = same slope Perpendicular lines = opposite, reciprocal slope Vertical lines = undefined slope ( Equation is x = a ) Horizontal lines = slope of 0 ( Equation is y = b) To find slope between two points on a line: Rise over run Change in y over change in x Use:

Slope Intercept: y = mx + b m= slope, b = y intercept Standard Form: Ax + By = C Point Slope Form: y – y 1 = m (x – x 1 ) m = slope, (x 1, y 1 ) = any point on the line

Need a point on the line and the slope of the line If given 2 points, find the slope first, then use either point Use algebra to move back and forth between forms of a line Example: Write the equation of the line that passes through the point (1, -5) and has slope -2.

X – intercept : y coordinate= 0 Y- intercept : x coordinate = 0 Can graph using intercepts or in slope-intercept form To graph in slope-intercept: graph the y-intercept, use slope to graph other points #33: Graph the equation: 4x + 8y = 32

Region of solutions Graph the boundary line first (dashed if > or or <) Choose a test point (use an easy point, such as (0,0)) Plug the test point into inequality. If it is a solution, shade the region where the test point lies. If it is not a solution, shade the area where the test point does not lie.

#38: Graph the inequality - y < 3x-5 1. Isolate y: y > -3x+5 2. Graph the boundary line y = 3x-5 3. Shade the appropriate area.

What does the solution to a system of equations represent? Can solve by graphing, elimination or substitution Many solution same line One solution point of intersection No Solution lines are parallel The point of intersection of the 2 graphs of the equations.

#40: How many solutions does the system have? x – 4y =2 2x-8y= 5 #42: Solve the system. 3x + 4y = 4 3x + y = 10

Graph each inequality separately and shade. The solution region is where the shading for all inequalities in system overlap. # 54: Graph the system: x > 1 y < -5

Real Number System Whole Numbers 0, 1, 2, 3, …….. Integers …..,-2, -1, 0, 1, 2, 3,……….. Rational Numbers- numbers that can be written as a ratio of two integers. Irrational Numbers – numbers when written as decimals that do not terminate or repeat.