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Algebra 1: Solving Equations with variables on BOTH sides
Do Now Solve the following equations: 2x+5=8 8x+2x+5=10 2x+3=5x 16 – x = 12 – 3x
Do Now Answers: 2x+5=8 Answer: x = 3/2 8x+2x+5=10 Answer: x = 1/2 2x+3=5x Answer: x = 1 16 – x = 12 – 3x Answer: x = -2
Equations vs. Expressions What’s the difference?
Expressions vs. Equations Equations: Have an equals sign! They can be solved. Examples: y+2=x 5+x=9 Expressions: Do not have an equals sign. They can only be simplified. Examples: 2x+3y 5y+2y+8
Solving Equations Steps: Simplify the left side of the equation Simplify the right side of the equation CLT (Combine Like Terms) Solve!
Example 1: 2x + 4x + 4 + 6 = 12 + 3x + 5x + 14
Checking Solutions You can easily determine whether you are right by substituting your solution back into the original equation! We got x = - 8. So let’s see if it works! 2x + 4x + 4 + 6 = 12 + 3x + 5x + 14
4x + x + 2 = 5x – 4 + 6 Example 2:
WHAT?!?!?! We Got that x = x. So what is our solution?!?!
Example 3: x + 4x + 2 + x = 6x
WHAT?!?!?! We got 0 = 2? What’s the solution to this problem?
Notice….. Equations can have three types of answers: One Solution Infinitely Many Solutions No Solutions
Practice Try some on your own!
Exit Ticket Solve the following problem– how many solutions does it have? x + x + x + 3x + 8 + (2 * 6) + (2 2 )= 5x + 2 * 6
8-2: Solving Systems of Equations using Substitution
Solving Quadratic Equations by Factoring Algebra I.
Solving Equations In Quadratic Form There are several methods one can use to solve a quadratic equation. Sometimes we are called upon to solve an equation.
Solve an equation with variables on both sides
Copy and complete using a review term from the list below.
Solve an equation by combining like terms
Table of Contents Solving Equations In Quadratic Form There are several methods one can use to solve a quadratic equation. Sometimes we are called upon.
3.5 Solving systems of equations in 3 variables
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3.1 Solving Linear Systems by Graphing
Graphing Systems of Equations Graph of a System Intersecting lines- intersect at one point One solution Same Line- always are on top of each other,
1. solve equations with variables on both sides. 2. solve equations containing grouping symbols. 3.5 Objectives The student will be able to:
Warm Up Simplify each expression. 1. 3x + 2y – 5x – 2y
Solving Linear Systems by Substitution Section 3-2:
3-2 Solving Equations by Using Addition and Subtraction Objective: Students will be able to solve equations by using addition and subtraction.
Solving Multi- Step Equations. And we don’t know “Y” either!!
Solve an equation by combining like terms EXAMPLE 1 8x – 3x – 10 = 20 Write original equation. 5x – 10 = 20 Combine like terms. 5x – =
InequalitiesInequalities. An inequality is like an equation, but instead of an equal sign (=) it has one of these signs: Inequalities work like equations,
5.3: Solving Addition Equations Goal #1: Solving Addition Problems Goal #2: Writing Addition Equations.
3.1 Solving Linear Systems by Graphing 9/20/13. Solution of a system of 2 linear equations: Is an ordered pair (x, y) that satisfies both equations. Graphically,
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