Ch 13 Linear Equations

Ch 13 Linear Equations

What is a Linear Equation?

• A linear equation is an equation that contains letters and numbers, for example 3x+10=16. It does not contain any x2 or x3 terms.

• By writing an expression equal to a constant or another expression, we create an equation; for example, 2x+5=7, 3y−4=y+6 are equations

Multiple Select

Which of these is a linear equation?

Hint: There are 2 correct answers.

• 2x + 7 = 10

• x² + 2 = 0

• x + y

• x³ + 9 < 1000

• 3x + 9 = x + 1

Open Ended

Write an equation to represent each of these puzzles.

I am thinking of a number.

When I multiply the number by 8, the answer is 24.

Hint: Let the number be any letter.

Open Ended

When I divide the number by 5, the answer is 7.

Open Ended

When I subtract 7 from the number, the answer is 25.

Open Ended

When I subtract the number from 72, the answer is 52.

Open Ended

When I square the number, the result is 36.

Solving the equation by close inspection.

i.e. without writing any calculations or using calculator.

x - 10 = 10

Fill in the Blanks

Solve the following equations through close inspection.

 $\frac{w}{3}\ =\ 4$  

Fill in the Blanks

Solve the following equations through close inspection.

h - 9 =10

Fill in the Blanks

When I divide 60 by the number, the answer is 10.

Guess, check and improve

We can try to guess the solution to an equation.

By noting the result when we substitute each guess, we can improve the guess and come closer to the solution.

The method can also be used to find the value of 2 different variables in an equation.

Fill in the Blanks

Find the missing number.

? + 6 = 9

Fill in the Blanks

? - 5 = 2

Fill in the Blanks

X 4 = 12

Fill in the Blanks

 $15\ \div\ \ ?\ =\ 3$  

Fill in the Blanks

3 + ? = 8

Fill in the Blanks

7 - ? = 3

Fill in the Blanks

9 X ? = 27

Fill in the Blanks

 $?\ \div\ 2\ =\ 4$  

Fill in the Blanks

7 - ? = 0

Fill in the Blanks

5 X ? = 5