Linear Equations and Inequalities notes
36 notes by 30 users
This GoConqr page gathers notes on equations, inequalities, slope and graphs. They are for school students practising algebra and teachers looking for material to use in lessons. There are over 20 notes from more than 20 users, mostly at school level. Pick a note that matches your topic to get started.
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- Properties of Equality9
- Solving Linear Equations in One Variable81
- Absolute Value Equations8
- Solving Inequalities in One Variable22
- Linear Equations in Two Variables30
- Slope of a Line27
- Forms of the Equation of a Line48
- Parallel and Perpendicular Lines8
- Linear Functions and Direct Variation6
- Systems of Linear Equations79
- Graphing Linear Inequalities5
Notes
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Algebra 2- Solving Equations and Expressions 1-1 Expressions and Formulas Questions: Find the value of each expression. (Note: Use Order of Operations, PEMDAS)1. 8(3+6)  ...
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Maths revision Chapter 2. Chapter 2 An equation is a statement that two things are equal, such as: 2 + 2 = 4 7 x 5 = 30 + 5 4 + x = 10 + y It consists of 2 expressions separated by the equal signs (=+, and it is considered true if the left han...
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Solving multi-step equations! Solving Equations! ( aka solving a mystery!) What are one step equations? How do they look? What are the four basic operations? One step means you have to do only one thing to find an answer! ...
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Solving multi-step equations! Solving Equations! ( aka solving a mystery!) What are one step equations? How do they look? What are the four basic operations? One step means you have to do only one thing to find an answer! ...
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Linear inequalities with one unknown Inequalities with an unknown Inequalities An inequality is an inequality between algebraic expressions. For inequalities we will use the symbols: (less than); (greater than); (less than or equal to) and (greater than ...
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Untitled Algebra 1 - Solving Multi Step Equations 8-3-2022 To solve multi step equations, you form a series of simpler equations. To do this, use the properties of equality, inverse operations, and properties of real num...
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2*2 Simultaneous Equations What are they?1) We have 2 systems of equations.1b) This means we're basically finding 2 solutions that fit both equations.1c) Those 2 solutions will be x and y, which are 2 points, (The points of intersection)Work it...
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1.4 Quadratic Equations Quadratic Equations The standard form of a Quadratic Equation is (ax squared +bx + c = 0)a,b, and c are real numbersA Quadratic Equation is a second-degree equation Zero-Factor Property If ab = 0, then a = 0, or b = 0...
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Quadratic Inequality
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1.7 Inequalities
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Untitled Equation of a straight line Example 12 Find the value of the gradient and y-intercept for these relations and sketch their graphs. Y = 2x – 1 Gradient = 2 = 2/1 Label the y intercept at (0, - 1). From the gradi...
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Slope What is slope and how do you find it? Slope is the rate of change between wo points on a line. ( slope = steepness of a line). To find slope of a line find the ratio of the change in y to the change in x. (Δy/Δx) the ...
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Solving multi-step equations! Solving Equations! ( aka solving a mystery!) What are one step equations? How do they look? What are the four basic operations? One step means you have to do only one thing to find an answer! ...
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Solving Linear Equation Example 1: Solve for g. -10 − 10g = -12g + 12 2g − 10 = 12 Add 12g to both sides 2g = 22 Add 10 to both sides g = 11 Divide both sides by 2
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Steps to Solving Various Equations Quadratic Inequalities Move everything to one side Factor Find critical numbers Plot critical numbers on number line Test each interval Write sets in interval notation Rational Inequalities
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Algebra One-Step Equations:a + bx = c Two-Steps Equations: ax + b = c Two-Steps Equations: x ÷ a + b = c
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Cheat sheet
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Algebra If I had to say anything to say when you click the button, I would've said, please finish this until the end which might take one day. Then do the quiz. Algebra is a type of algorithm that allows you to find...
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Math Direct Variaition Notes - 3.4 Lesson 3.4: Direct Variation W.A.L.T. write and graph direct variation equations solve problems involving direct variation &...
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The Slope of a Line Vocabulary Terms Slope: The ratio of a lines verticle change (rise) to it's horizontal change (run)Rise:- A lines verticle change- y-intercept- outputsRun- a line's horizontal change
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1.6 Other Types of Equations & Applications Rational Expressions A Rational Expression is an equation that has a rational expression for one or more terms.To solve multiply each side by the Lowest Common Denominator.The value of the variable that appears to be ...
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Untitled Unit 1: 1-1 Operations With Equations Vocabulary Used in Section: Variable: A letter or a symbol used to represent a value that can change Example: x,z,a,&n...
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Intro to second semester equations and solutions ~ solutions: a value for a variable that makes an equation true ~solving and equation = the process of finding the solution. We want the variable by itself. ~Inverse operations to "undo" ...
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Linear Equations & Applications What is a Linear Equation? A Linear Equation has to be able to be written in the form ax+b=0a and b cannot equal 0a and b have to be Real Numbers How to Solve Linear Equations Get rid of ( ) Collect like terms on each...
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SOLVING EQUATIONS (1.3)
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Solving Linear Equations Graphing Visual display Estimate a solution Substitution One equation is already solved for one of the variables It is easy to solve for one of the variables Elimination Coefficients of one variable are same or opposi...
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Graphs Graphs of linear relations X = I - independent (time is always)Y = D - dependent (cost,pay, height)Always put title and label everythingIf not starting at 1 but a "break" to show Y = 2xwhat is the value of Y if X = 3Y...
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Equation of Lines - created from Mind Map Given slope and y-interceptSubstitute m and b into the equation y=mx+b Given slope and a pointFind b by substituting m and the (x,y) into the y=mx+b format, then use the m and b in the new equation Given 2 points
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Linear Equations - created from Mind Map Standard Form Slope Intercept Form Point Slope Form
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Pair of Linear Equations in two Variables - created from Mind Map General form Solution Graphically Algebric Methods
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Properties of Equality - Addition & Subtraction
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Writing Inequalities Writing Inequalites Chapter 4 Section 1Writing inequalitesVocabInequality - Different in size [IN]=Un=Not [Equality]=Equal
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Equations of parallel and perpendicular lines Perpendicular lines are lines that intersect at 90° and if 1 line's equations are 1/3 then the equation of the perpendicular line is -3/1
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Pair of Linear Equations in Two Variables - created from Mind Map DbfbdxbxndjzjsWfwxww General Form Solutio Graphically
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Rules of inequalities
More Linear Equations and Inequalities resources
About linear equations and inequalities notes
GoConqr OriginalUsing linear equations and inequalities notes
For a worked example, start with Solving Linear Equation. It shows how to work through an equation with the unknown on both sides. If you are revising inequalities, the notes on inequalities explain what happens to the inequality sign when you multiply or divide by a negative number.
Other notes cover simultaneous equations, quadratic inequalities and the slope of a line. Writing Inequalities offers another place to look when that is your focus.
Make the notes part of revision
Read through an example, then cover the steps and try to follow them yourself. Return to the note to check your working. If you want to test a topic after reading, switch to a quiz on the unit page. A mind map can help you review how ideas connect, while flashcards offer another way to revisit them.
Choose a note and work through it at your own pace.
Frequently asked questions
Which note is a useful starting point for solving equations?
Solving Linear Equation is a useful starting point if you want to follow a worked example. It shows an equation with the unknown on both sides and sets out the steps used to solve it. There are also notes on expressions and formulas if you want to practise evaluating expressions.
Do these notes cover inequalities as well as equations?
Yes. The listing includes Linear inequalities with one unknown, Writing Inequalities and Quadratic Inequality. There are also notes explaining inequality rules, including when the direction of the inequality sign changes. For equations, the page includes worked material on linear and simultaneous equations.
Are the notes free to use?
Yes. Every note listed here is free to open and study without an account. The resources were made by GoConqr users rather than GoConqr. A free account also lets you make your own notes, quizzes, mind maps and flashcards, and saves your quiz scores.