Solving equations The balancing method

Slides:

Advertisements

Similar presentations

Equations with the unknown on both sides.

Advertisements

For Educational Use Only © 2010 Benchmark 10 I can solve absolute value equations.

Solving 2 Step Equations

Unit 14 SIMPLE EQUATIONS.

Introduction To Equation Solving. xx 2x + 1 = 4 Solve :

Intro to Algebra/Geometry Solving Equations by Adding or Subtracting.

Solving 2-step equations ax + b = c. Keep it balanced Just like when solving a one- step equation keep it balanced. Just like when solving a one- step.

Solving Equations Grade 5 Math.

ALGEBRA REVIEW QUESTIONS. = balance = It is important to understand that every equation is a balancing situation. Everything on the left of the equal.

Subtracting Across Zeros

EQUATIONS This presentation accompanies the worksheet: “Simple equations” available at:

Solving equations Section 1.4.

Whiteboardmaths.com © 2008 All rights reserved

Proportions Round One 2) x + 3 = 15 Answers 2.) x + 3 = 15 X=12 21.

Solving Equations. What will happen if you add or subtract an equal amount of weight on both sides of the scales? Solving equations is like balancing.

Section Writing Equations. Translating Sentences into Equations Look for key words or phrases that represent “equal to”. The following all mean.

3.1 – SOLVING EQUATIONS BY USING ADDITION AND SUBTRACTION.

Algebra Solving Linear Equations 3 x = 6 x = 2 Change side,change sign.

Solving Equations A “Balanced” Approach Skip to Integer Practice Skip to One-Step Equations Skip to Two-Step Equations.

Objective The student will be able to: solve equations using addition and subtraction.

Solving Equations by Adding or Subtracting Objective: Solve equations using the addition and subtraction properties of equalities.

6.6 Solving Radical Equations. Principle of power: If a = b then a n = b n for any n Question: Is it also true that if a n = b n then a = b? Explain in.

Solving Algebraic Problems. Step One Consider the order in which the equation was built. 3x + 8 = 5 4 x Was the “x” multiplied or divided by anything?

The Equation Game. Why is an equation like a balance scale? 3 2x - 1 =

Equation y + 5 y + 5 = 20 Expressions

Solve equations using addition and subtraction.

Solving Equations When do we use solving equations? We use solving equations methods when we know what the problem equals but not what the variable is.

Solving Addition Equations SWBAT solve addition equations using the subtraction property of equality.

Example 1 Solving Two-Step Equations SOLUTION a. 12x2x + 5 = Write original equation. 112x2x + – = 15 – Subtract 1 from each side. (Subtraction property.

One-Step Equations I can show that solving an equation leads to finding the value that makes the equation true.

Small Square Value = 1 Rectangle x Value = x Large Square x x Value = x 2 Algebra Tiles.

Table of Contents First get all nonzero terms on one side. Quadratic Equation: Solving by factoring Example: Solve 6x 2 – 13x = 8. 6x 2 – 13x – 8 = 0 Second.

CLICK THE NUMBERS IN SEQUENCE

Solving Equations. To solve an equation, you must isolate the variable (get the letter by itself). You do this by using opposite operations to undo what’s.

Solving Two-Step Equations What IS A TWO STEP EQUATIONS? What you do to one side of the equation must also be done to the other side to keep it balanced.

By, Mrs. Muller.  Recall the following properties when solving these types of equations:  Addition property of equality: a=b, then a+c=b+c, or 2x3=6,

Double-Digit Addition Strategies

Solving Inequalities Using Addition & Subtraction.

Callum thinks of a number, adds 7 and the answer is 16. Represent this statement as an equation and hence solve the equation. Verify your answer.

Solving equations with variable on both sides Part 1.

Continue the sequence 1. ½, 1, 2, 4, 8, __, __, __ 2. __, 5, 9, 13, __, __, , 55, __, 15, __, __ 4. 8, 27, 103, __ 5 Minutes Remain.

* Collect the like terms 1. 2a = 2a x -2x + 9 = 6x z – – 5z = 2z - 6.

Solving 2 step equations. Two step equations have addition or subtraction and multiply or divide 3x + 1 = 10 3x + 1 = 10 4y + 2 = 10 4y + 2 = 10 2b +

Do Now. Unit 2, Lesson 1 SWBAT solve one step equations using adding and subtraction SWBAT solve two step equations using inverse operations.

Two-Step Equations Review 1-Step 2-Step Equations Practice Problems.

Intro to Expressions & Equations ___________________________________________________ __________ Algebra 1 – Solving Equations - Math is Hip ™ Prerequisite.

___________________________________________________ _______ Algebra 1 – Solving Equations - Math is Hip ™ Prerequisite Skills Needed: - Basic Addition.

Balancing Equations The student will be able to: solve equations using addition and subtraction.

Substitution Method: Solve the linear system. Y = 3x + 2 Equation 1 x + 2y=11 Equation 2.

Standard 14 Solve by completing the square. Example One. Instructions: Factor Perfect Square.

A geologist has 10 rocks of equal weight

Factoring Review.

Factoring Review.

ONE STEP EQUATIONS.

ONE STEP EQUATIONS.

Variables on Both Sides with Equations

Solving Equations A “Balanced” Approach Skip to One-Step Equations

Solving Equations by Factoring and Problem Solving

NUMBERS one two three four five six seven eight

Solving Equations Grade 5 Math.

Section 2.9 Solving One-Step Inequalities by Adding or Subtracting

a + 2 = 6 What does this represent? 2 a

CLICK THE NUMBERS IN SEQUENCE

Think about… How is an equation like a balance scale?

ONE STEP EQUATIONS WHAT?!?!.

ONE STEP EQUATIONS.

CLICK THE NUMBERS IN SEQUENCE

Multiplication facts Your Help Guide.

ONE STEP EQUATIONS.

Balanced scales and equations

Presentation transcript:

Solving equations The balancing method An equation means that two things are equal. If the scales balance, then the value of each side must be equal.

Two bags of x marbles plus five extra marbles equals 21 marbles. If we remove a marble from one side, we must remove a marble from the other side so that the scales still balance. x x 2x + 5 = 21 2x + 4 = 20

The scales now show that two bags of x marbles plus four extra marbles equals 20 marbles. We can continue to remove marbles, as long as we do the same thing to each side. x x 2x + 5 = 21 2x + 4 = 20 2 3 1 16 19 18 17

The scales now show that two bags of x marbles equals 16 marbles. We can’t remove any more marbles, but we can halve the values on each side. ÷ 2 ÷ 2 x x 2x + 5 = 21 2x = 16 x = 8

2x + 5 = x + 10 2x = x + 5 x = 5 Try another one: Two bags of x marbles plus five extra marbles equals one bag of x marbles plus ten extra marbles. x x x 2x + 5 = x + 10 Remove 5 marbles. 2x = x + 5 Remove a bag of marbles. x = 5

2x + 6 = x + 9 2x = x + 3 x = 3 Try another one: Two bags of x marbles plus six extra marbles equals one bag of x marbles plus nine extra marbles. x x x 2x + 6 = x + 9 Remove 6 marbles. 2x = x + 3 Remove a bag of marbles. x = 3

Whatever we do to one side of the equation we must do to the other. When solving equations, try to imagine the scales. To make sure the equation balances … Whatever we do to one side of the equation we must do to the other. 2x + 6 = x + 9 Example 1: 2x + 6 = x + 9 -6 2x = x + 3 -x x = 3 2x + 6 = x + 9 -x x + 6 = 9 Does it matter if you subtracted the x or the number first? -6 x = 3

Whatever we do to one side of the equation we must do to the other. When solving equations, try to imagine the scales. To make sure the equation balances … Whatever we do to one side of the equation we must do to the other. 8x – 5 = 11 Example 2: 5p – 17 = -2 Example 3: + 5 + 17 8x = 16 5p = 15 ÷ 8 ÷ 5 x = 2 p = 3 3x – 5 = x + 11 Example 4: 7q – 6 = 3q + 10 Example 5: + 5 + 6 3x = x + 16 7q = 3q + 16 - x - 3q 2x = 16 4q = 16 ÷ 2 ÷ 4 x = 8 q = 4

Whatever we do to one side of the equation we must do to the other. When solving equations, try to imagine the scales. To make sure the equation balances … Whatever we do to one side of the equation we must do to the other. Solve the following equations: 3x + 8 = 20 7x – 9 = 26 5x – 40 = -5 3x + 7 = x + 11 6x + 5 = 4x + 10 5p – 3 = 2p + 9 4y – 7 = 2y – 9 x = 4 x = 5 x = 7 x = 2 x = 2.5 p = 4 y = -1