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Multiply and divide two-step linear equations

PAT: Master Provincial Achievement Test Skills

Operations with Decimals

test

Adding and subtracting decimals

Subtracting Decimals — Data Table

Ordering Decimals — Data Table

Decimals – Word Problem

Adding Decimals

Subtracting Decimals

Multiplying decimals

Multiplying Decimals

Dividing decimals 

Dividing Decimals

Order of operations (BEDMAS)

Mixed Operations with Decimals

Mixed Operations

Identify the Order of Operations

Order of Operations — Word Problem

Mixed Operations with Decimals Bracket

Mixed Operations with Bracket Square

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Square Roots

Squares and square roots

Square Root of a Perfect Square

Estimating square roots

Rational Numbers

Comparing and ordering rational numbers

Comparing decimal numbers

Comparing fractions

Solving problems with rational numbers in decimal form

Solving problems with rational numbers in fraction form

Operations with fractions

Determine square roots of rational numbers

Square roots of rational numbers

Powers and Exponents

Using exponents to describe numbers

Expanded powers

Exponent rules

Single Power Expressions

Dividing powers

Multiplying powers

Order of operations with exponents

Using exponents to solve problems

Introduction to Linear Relations

Understanding graphs of linear relationships

Linear relations

Understanding tables of values of linear relationships

Linear relation

Applications of linear relationships

Linear Relations

Representing patterns in linear relations

Represent Patterns in Linear Relations Equation Decimal

Represent Patterns in Linear Relations Equation Integer Start From 0

Represent Patterns in Linear Relations Equation Integer Start From 1

Represent Patterns in Linear Relations Equation Negative Decimal

Identify the Linear Equation

Reading linear relation graphs

Solving linear equations by graphing

Solving Linear Equations

Solving linear equations using multiplication and division

Two-step Linear Equations LHS

Two-step Linear Equations RHS

Solving two-step linear equations: ax + b = c, x/a + b = c

Solving two-step linear equations: ax + b = c, x/a + b = c

Solving linear equations using distributive property: a(x + b) = c

Solving linear equations using distributive property: a(x + b) = c

Solving linear equations with variables on both sides

Model and solve one-step linear equations: ax = b, x/a = b

One-step Linear Equations

One Step Linear Equations — Word Problem

One-step equations

One-step Equations LHS

One-step Equations RHS

Model And Solve One Step Linear Equations Divide – Word Problem

Model And Solve One Step Linear Equations Multiply – Word Problem

Solving two-step linear equations using addition and subtraction: ax + b = c

Two-step Linear Equations

Solve Linear Equations Using Addition and Subtraction – Word Problem

Two-step Linear Equations — Word Problem

Solving two-step linear equations using multiplication and division: x/a + b = c

Solving two-step linear equations using distributive property: a(x + b) = c

Solve Linear Equations Using Distributive Property – Word Problem

Introduction to Polynomials

Characteristics of polynomials

What are polynomials

Equivalent expressions of polynomials

What is a polynomial?

Classifying Polynomials

Polynomial components

Operations with Polynomials

Adding and subtracting polynomials

Multiplying and dividing monomials 

Divide a monomial by a monomial

Multiply a monomial by a monomial

Multiplying polynomials by monomials

Multiply a polynomial by a monomial

Dividing polynomials by monomials

Circle Geometry

Angles in a circle

Chord properties 

Tangent properties

Surface Area of 3D Objects

Surface area of 3-dimensional shapes

Introduction to surface area of 3-dimensional shapes

Nets of 3-dimensional shapes

Surface area of prisms

Surface Area of Prisms Rectangle

Calculate the Surface Area

Surface area of cylinders

Scale Factors and Similarity

Enlargements and reductions with scale factors

Scale diagrams

Similar triangles

Similar polygons

Symmtery

Line symmetry

Rotational symmetry and transformations

Influencing factors in data collection

Data collection

Probability

Provincial Achievement Test

sample

math

https://dmn92m25mtw4z.cloudfront.net/img/textbook/textbook-ca-pat.png

Ex. 1:

Ex. 2:

Ex. 3:

Solving -x/8 - 3 = 24 using a visual model and algebra

Solving x/4 + 2 = -10 using a visual model and algebra

- So we have another question here. It says, three plus X over four. And that's the equivalent to 51, right? 
So to solve the X, which is standing right there. You want to remove the things that are further away from it. So then the first thing you do is you want to get rid of the three. So the three has to be removed. How do we do that? That's a positive three. So to remove it, we have to subtract the three from both sides. So by doing that, negative three, negative three. That canceled the three here. You're left with just the X over four. And over here it's 51 minus 3. That gives you just 48. So the last step right here to solve the X is that we have to get rid of the four underneath. This has been divided so we do the opposite by multiplying by a four. Let me just put the four in brackets. It means that they're being multiplied. So what happens, the fours here cancel, and you're left with just the X. And it's equal to 48 times 4. Quickly punch in my calculator. I got a 192. And this is your final answer for this question. Thanks for watching.

Solving x/a + b = c when terms are in reverse order

Solving x/(-2) + 10 = 17 by isolating x

Solving x/(-6) - 21 = -9 using inverse operations

Solving x/8 + 23 = -1 using subtraction then multiplication

Ice cube melting time word problem using substitution

Finding the temperature for an ice cube to melt in 5 minutes

Continue from the previous section, we will solve linear equations in diagram, equation, and word problems forms. However, in addition to subtraction and addition, we will teach you how to solve linear equations that also involve multiplications and divisions. 

Solving linear equations using multiplication and division: x/a + b = c

Solving two-step linear equations using multiplication and division x/a+b=c

Solving two-step linear equations using multiplication and division: x/a + b = c

Dividing integers

Solving two-step linear equations using multiplication and division: x/a + b = c

What You'll Learn

Solve two-step linear equations involving division and addition/subtraction

Apply reverse BEDMAS to isolate variables by undoing operations in correct order

Work with equations in the form x/a + b = c and variations with negative terms

Multiply both sides by the denominator to eliminate fractions

Verify solutions by substituting values back into original equations

What You'll Practice

Solving equations with variables divided by positive and negative numbers

Isolating x when equations are written in reverse order

Working with real-world word problems involving formulas and substitution

Handling equations with negative coefficients and multiple operations

Why This Matters

Before You Start — Make Sure You Can:

This Unit Includes

8 Video lessons

Practice exercises

Skills

Two-Step Equations

Division

Multiplication

Reverse BEDMAS

Isolating Variables

Linear Equations

Word Problems