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# Linear Equations

LINEAR EQUATIONS

PART 1

The magic of equations

Think of a number.

Multiply it by 2

Subtract 4

Divide the result by 2

If you subtract the number you initially thought of, do you obtain 3?

Warm-up thought

Looking at the balanced scale, could you find out the weight of the red rectangle provided that each blue circle weighs 100 g?

Now, can you explain how did you find out the answer?

Practice with symbols

Join the given words with the operator used in equations:

add, addition, sum, increased by, subtraction, difference, minus, decreased by, less, multiplication, product of, multiplied, times, division, quotient of, divide by, is/are, gives, equals, total

 + - * / =

Variables, expressions and equations

A variable is a symbol that represents a number. Usually we use letters such as x or y for variables. We treat x as if it were a number we could use. For example, if x is the height of a tree, a tree that doubles the height of the former tree will have a height of 2*x.

An expression is a mathematical term (or a combination of mathematical terms using operators) that may use numbers, variables, or both. For example, 5+2x-1*3.

An equation is a statement that two numbers or expressions are equal. Equations are useful for relating variables and numbers. Many real-life problems can easily be written down as equations. There are steps to solve equations.

Equation maker

The variables are symbol that represent an unknown value. The objective of the equation is to find the value of the variable that makes the equality be true.

Now, write an equation based on the following sentences. The first one is an example. The letter x is used as variable..

1. Three times a number is nine.

3 x = 9

2. Four times a number minus seven equals nine plus minus four thimes the number.

3. Six plus a number totals five.

4. Minus twelve divided by a number is four.

5. Three plus four times a number equals minus one.

A break to feed the brain

Watch the following video about how to solve linear equations:

Can you now solve the equations you wrote in the equation maker exercise? If not yet, please watch the videos Solving Equations #2 and Solving Equations #3 attached to this unit.

Now, nothing stops you! Solve the equations you built previously.

PART 2

Writing down the ideas for solving linear equations

Steps to solve linear equations. Complete the exercise "Steps" in this unit.

Then, complete the exercise "Steps practice".

Practice makes the master

Find the value of x in the following linear equations. Try to identify the steps you are using.

a) 3x = 24

b) 4x + 7 = 23

c) 2 + 3x = -10

d) 2 / 4x - 1 = 3

e) 36 = 6 (x - 6)

f) 80 = 9x - 1

g) 2 (x + 4) = 12

h) 3x - 2 / 5 = 2

i) 25 - 3x = 1 + 3 (4 + 3x)

j) x / 2 + x / 5 = 10 / 7

PART 3

Rule the real world

The aim of equations is to help us solve problems from the real life. Find the answer to these questions.

a) You pay 10€ each month to join a gym. Unfortunately, the cycling class is not included so you pay 3€ each time you go to this activity. At the end of the year, you have paid 171€. How many times did you go to the cycling class this year?

b) The height of three trees are three consecutive numbers and the sum of the three heights is 33. What is the height of the three trees?

c) With the money I have now, I need 1.8€ more to buy my favourite magazine. If I had two times the money I have now, I would have 2€ left after buying it. How much does the magazine cost? How much do I have? (You may use more than one equation and variable)

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