# LESSON1 - EQUATION

## INTRODUCTION TO EQUATIONS

**What are equations?**

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**Equations are made up of two expressions on either side of an equals sign, like**

**x + 2 = 1**

**To solve an equation, you need to find the values of the missing numbers.**

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**"I think of a number, add four, and the answer is seven"**

**Written algebraically, this statement is x + 4 = 7 , where x represents the number you thought of.**

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**x + 4 = 7 is an example of an algebraic equation, x represents an unknown number.**

**The number you first thought of must be three (3 + 4 = 7). Therefore, x = 3 is the solution to the equation x + 4 = 7.**

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** More complex equations !**

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**Sometimes an equation will have multiples of an unknown, e.g 5y = 20. To solve this you need to get the unknown on its own. To do this, divide both
sides by 5.**

**5y = 20**

**5y ÷ 5 = 20 ÷ 5**

**y = 4**

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### USEFUL PHRASES

**satisfy an equation- - spełnia równanie**

**substitute 2 for x - podstawic 2 za x**

**cancel equal terms - sktócic jednakowe wyrazy**

### LABEL TRUE OR FALSE

**Equations in physics show how quantities are related. To use formula you replace the known variables with the given values in order to find the unknown
variable. (T/F)**

**A stroke through an equality symbol negate it. ( T/F)**

### SELECT THE PHRASE

**that best completes the sentence: must be, cannot be, can be but needn't be**

**The solution set of an equation .................................the empty set.**

**The like terms ..................... combined before solving the equation**

### FILL IN THE GAPS

**Before solving an equation like 6x + 2x + 5 = 25, you should first .................... the .................. terms.**

**The ........................... set of an ........................ is the set of all numbers that are ................... of this equation.**

### Say, if the sentence is true always/sometimes/never

**After replacing a variable with number an open sentence becomes true or false.**

**A linear equation in one variable has exactly one root**

####
**Real-World
Connection**

**You are ordering tulip bulbs from a flower catalog. You have $14 to spend. If the shipping
cost is $3.00 for any size order, determine the number of bulbs you can order.**

### Solve equations !

**1) 8p - 3 = 13**

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**2) -n + 8.5 = 14.2**

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**3) 6(t + 5) =
-36**

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**4) 7h + 2h - 3 = 15**

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**5) -3(5 - t) =
18**

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**6) 0.1(h +
20) = 3**

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**7) 4 -
y = 10**