WEEK 9-SOLVING-MULTI-STEP-ONE-VARIABLE-EQUATIONS

Solving Multi-Step One Variable Equations

Objectives

Start

Story

Properties of Equality

Solving Linear Equations

Solution of x² = p and x³ = q

Summary

Story

Reviewing Properties of Equality

Properties of Equality

Let x,y,z be real numbers, the following properties hold:

If x=y then

x=x

x=y --> y=x

If x=y then xz=yz

Properties of =

If x=y then x-z=y-z

x=y and y=zthen x=z

If x=y thenx+z=y+z

Why are properties of equality important?

Because they allow us to find the solutions of almost any equation!

Solving Linear Equations

Let's see some examples:

Example 2: Multi-step equation Solve

Example 1: Two step equation Solve

3(x - 2) + 8 = 20

5x+6=16

x=2

x=6

It’s important to check if our solutions make sense. They've told me to substitute back into the original equation.

🗨️

Example 2: After solving 2(x+1) + 1 = 11, Julian found the solution x = 6. Is it correct?

2(6+1) + 1 = 2(7)+1 = 15 ≠ 11

x=6 is not correct.

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• 2(x+ 1) + 6 = 18 x = 5
• 4z - 7 = 13 z = 5
• 3(x + 1) = -15 x = -6
• 5x = 3(x-1) + 9 x = 3

Link the symbols with their meaning

The solution will appear in 30 seconds

2(x+ 1) + 6 = 18

x = 3

4z - 7 = 13

x = 5

3(x + 1) = -15

x = -6

5x = 3(x-1) + 9

z= 5

Solution of x² = p and x³ = q

Let's consider the following problem:

What number squared equals 4? As an equation, Find x in:

x²=4

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There are two solution of

The first is because 2·2 = 4

x²=4

x=2 ,

But there's another one: because (-2)·(-2)=4

x=-2 ,

Any equation of the form x²=a has two solutions

Proposition: The solutions of the equation x²=a are

Example 1: Find the solutions of

Here:

x²=9

is the unknown

Solutions are:

is any number a≥0

On the contrary, an equation of the form x³ = a has a single solution.

Proposition: The solution of the equation x³=a is

Example 1: Find the solutions of

Here:

x³=8

is the unknown

There is only one solution:

is any real number

x=2

Let's see some examples:

Example 1: Two step equation Solve

Example 2: Multi-step equation A square has an area of 16 u². Find the side of the square stating an equation, solve it.

x³=-27

Verifying:

x=-3

s=4

Try it by yourself:

Summary: Solving One-variable Equations

Great job!

See you next time

Welcome 6th graders!

A journey soon begin through Social Science experiences!

8TH-INTRODUCTION-TO-RATIONAL-AND-IRRATIONAL-NUMBERS-EN © 2024 by CASURID is licensed under CC BY-NC-ND 4.0

MATERIAL

It is highly advised to have:

• Grid paper.
• Pencils of different colors.
• Eraser.
• A rule.
• A compass.
• A Protactor.
• A calculator.
• Geogebra installed on your phone/tablet/computer (or use online version).

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Check the Solution

Whether it makes sense or no.

Annotate/ underline/draw givens and question

"MA.8.AR.2 Solve multi-step one-variable equations and inequalities." MA.8.AR.2.1 Solve multi-step linear equations in one variable, with rational number coefficients. Include equations with variables on both sides. MA.8.AR.2.3 Given an equation in the form of x² = p and x³ = q, where p is a whole number and q is an integer, determine the real solutions. MA.K12.MTR.6.1 Assess the reasonableness of solutions.

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Solve equation

Using properties of equality

If it's a square or cubic equation...

Find possible solutions using square root and cubic root.

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Write the equation of your problem