Somerset Area School District / Overview



Section numbers (in parenthesis) refer to the section in the Algebra 1 book you can refer to for help. If you need additional help, check Mr.DelSignore’s website and Ms. Ritenour’s website for the notes for those sections. If you have internet access, any of these topics can be found on Khan Academy. Go to and type in the section heading. There you will find more videos to walk you through each of these topics.Also, you’re more than welcome to contact your teacher and we gladly help you with your work! Solving 1-Variable Equations (3.1 – 3.3)4099560247650Example:2x+35=4x-62x+3=54x-62x+6=20x-306=18x-3036=18x2=x0Example:2x+35=4x-62x+3=54x-62x+6=20x-306=18x-3036=18x2=x-411480377190Review: When solving equations, our goal is to solve for the variable, or to get it alone. We are looking to find the solution that makes that equation true. -30480194310Practice 1: Solve each equation.19. Two friends share the cost of a torpedo sub from?Em’s?Subs.? The base price of the sub is p and the cost of all of the extra toppings totaled $3.75.? Each person’s share was $6.15.? Write an equation to model this scenario.??Then find the base price of the torpedo sub.20. A group of people dined at a local Outback Steakhouse.? The total bill came out to be $125.00. Included in this amount was a 6% sales tax for a group over 5 people and a tip that was 19%.? Write the equation to model the total cost of the group’s meal and find the total prior to taxes.??Solving Inequalities (4.1-4.4)3368040631825Example 2: Solve and Graph-2x-7>4-2x+14>4-2x>-10x<5Example 2: Solve and Graph-2x-7>4-2x+14>4-2x>-10x<576200624205Example 1: Solve and Graph2x+4≥82x≥4x≥2Example 1: Solve and Graph2x+4≥82x≥4x≥2Review: Solving inequalities is identical to solving equations. The only exception is the multiplying and dividing rule. When you multiply or divide by a negative number (that was “attached” to the variable), flip the inequality sign.34305341532611135329202356Practice 2: Solve and graph each inequality.342900050203109144050431703329940322961091440321437034366201553210685801519555-8n+5+5n<17-8≤-6m+7m-6m+14≥-8m+62+5p≤-12+7p-4p-190≥61-6n+8n-125r-r<2406x-13>7-53x+48-x-8≤x-1-55<6x-3-71+3x3x-58≥0.53512820-306705137160-3600453535680-2074545243840-2074545Sarah was given a gift of $2500 to start her bank account. Currently, she pays $45 each month for her cell phone, $10 each month for various apps on her cell phone, $30 per month for gas in her car, and $50 per month for eating out at local restaurants. If she does not spend money on anything else or makes any other deposits into this account, for how many months can she continue to spend money on these purchases? Write and solve an inequality to show this situation.A student in Mr. Algebra’s math class is solving the inequality: 2x-4-7x<37. Below is their work. Explain what mistake was made, then correct the problem.78486049530Graphing Linear Equations (Slope-Intercept Form) (6.2)Review: Graphing Linear equations from slope-intercept form requires identifying two important pieces of information: the slope (m) and the y-intercept (b). The y-intercept is where the line starts, then the next points are found by using the slope in riserun format.-381000184150In #1:b = 4, so the line started at 4 on the y-axis.m = -53 from the starting point, the next one was down 5, right 3.0In #1:b = 4, so the line started at 4 on the y-axis.m = -53 from the starting point, the next one was down 5, right 3.512826095250In #2:b = 2, so the line started at 2 on the y-axis.m = 25 from the starting point, the next one was up 2, right 5.0In #2:b = 2, so the line started at 2 on the y-axis.m = 25 from the starting point, the next one was up 2, right 5.center6985Examples: -44196018161000416814015430500Practice 3: Graph each equation.center698500-4114802203450018592806413500409956010828005029200266700Given: m = -2; (1, -7)y-y1=mx-x1y--7=-2x-1y+7=-2x+2y=-2x-50Given: m = -2; (1, -7)y-y1=mx-x1y--7=-2x-1y+7=-2x+2y=-2x-5Writing Linear Equations (6.5)474726022059904686300544830647700720090right1588770Given: (3,6) and (2,4)m=y2-y1x2-x1=4-62-3=-2-1=2y-y1=mx-x1y-6=2x-3y-6=2x-6y=2x00Given: (3,6) and (2,4)m=y2-y1x2-x1=4-62-3=-2-1=2y-y1=mx-x1y-6=2x-3y-6=2x-6y=2x-525780201930Example: Given: m = 4, b =2Equation: y = 4x+2Example: Given: m = 4, b =2Equation: y = 4x+2Practice 4: Write the linear equation of equation for each, in slope – intercept form.m = 12, b = -1m = 32, through (-2, -3)m = 23, b = 2through (-5, 2) and (2, -5)through (5, -3) and (0, 4)m = -8, b = -4m = -95 and through (5, -4)through (0, -1) and (-4, -2)through (2, 2) and with slope of -3 4549140236220ExampleExample-259080381000GraphingBest when both equations are in y = mx+b.Graph both equations, look for the point of intersection.Answer: (x,y)00GraphingBest when both equations are in y = mx+b.Graph both equations, look for the point of intersection.Answer: (x,y)Solving Systems of Equations (7.1-7.3)368808010414000-335280127000SubstitutionBest when one equation is solved for x or y. Substitute expression in place of solved variable in the other equation so your equation only has one variable. Solve for this variable.Substitute the solution back into one of the original equations to find the other variable.Answer: (x,y)00SubstitutionBest when one equation is solved for x or y. Substitute expression in place of solved variable in the other equation so your equation only has one variable. Solve for this variable.Substitute the solution back into one of the original equations to find the other variable.Answer: (x,y)-342900109220EliminationBest when both equations are in Ax+By=C. Line up x and y; to eliminate, x and y need to have the same number, different sign (of the coefficient. If necessary, change equation(s) by multiplying through the equation by the same number. Add the equations together and solve for one variable.Plug that number back into one of the equations to find the other variable.Answer: (x,y)00EliminationBest when both equations are in Ax+By=C. Line up x and y; to eliminate, x and y need to have the same number, different sign (of the coefficient. If necessary, change equation(s) by multiplying through the equation by the same number. Add the equations together and solve for one variable.Plug that number back into one of the equations to find the other variable.Answer: (x,y)4552950-2456180left190500Practice 5: Solve each system of equations. Use any method. ................
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