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SOLVING LINEAR EQUATIONS
Equations and their components
An equation is an expression stating the equality of two algebraic expressions. This equality exists only when certain values are assigned to the letters.
For example, the equation:
x + 6 = 2x + 1
is true only when x = 5
On each side of the equal sign in an equation there is an expression
The addends that comprise the expressions are called terms.
The letters are called unknowns.
The values for which the equation is true are called solutions.
Solving first degree equations with one unknown
To solve a first degree equation with one unknown, you reduce the expressions and move the terms until the unknown is isolated.
Examples:
6x-4=5x+3
6x-5x=3+4
x=7
2x-6=4-3x
2x+3x=4+6
5x=10
x=10/5
x=2
7x 4 = 2 - 2x
Solving problems with help of equations
Equations are useful tools that can help you to solve problems.
Example: Watch the steps taken.
In a pride of 13 lions, there are 3 more females than there are males. How many lions and how many lionesses are there?
Step 1:Identify the known and unknown numbers:
Lions(x
Lionesses(x+3
Total (13
Step 2: Use an equal sign to state the relationship between the components of the problem.
Lions + lionesses = 13
x + (x + 3) = 13
Step 3: Solve the equation:
x+x+3 =13
2x = 13-3
2x=10
x=10/2
x=5
Step 4: Give a solution:
Lions ( x=5
Lionesses( x+3=5+3=8
Solution: There are 5 lions and 8 lionesses.
PROBLEMS INVOLVING EQUATIONS
There are 31 people in a cafe. How many men and how many women are in the caf if there are 5 more men than women?
If you add thirteen to two times a number, you obtain a result of 99. What is the number?
I think of a number, add 7, and then multiply the new total by 4. I get the same answer as if I had just multiplied the original number by 6. What number did I think of.
A bowl of cream costs eighty cents more than a pasty. Maria and Felisa bought one bowl of ice cream and two pasties for a total of 4.40. How much does a pasty cost? How much does a bowl of ice cream cost?
A box of figs weighs one kilo more than a box of strawberries. Together three boxes of strawberries and two boxes of figs weigh 12 kg. How much does each box weigh?
Calculate the dimensions of a rectangular plot of land, given that the plots length is 20 metres more than its width and the fence that surrounds the plot is 240 metres long.
In a classroom, a half of the students play football and a third of them play basketball. If there are 4 students left playing tennis, how many students are in the classroom?
A bus with 130 passengers arrives at a station where an unknown number of passengers get off. At the next station, QUOTE of the passengers that are on the bus get off. If 40 passengers are now left on the bus, how many passengers got off at the first station?
John is five years older than his brother. In four years, John will be twice as old as his brother is now. Find out how old is John now.
Annas parents are 45 and 40 years old. If you add 3 to Annas age, you obtain a fifth of the sum of her parents ages. How old is Anna?
Your uncle is 27 years older than his son and in 12 years he will be double his son s age. How old are each of them?
3 kilos of coffee, which cost 16 per kilo, are mixed with 5 kilos of a different type of coffee, which costs 12 per kilo. How much does a kilo 8P Z [ )
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If you multiply a number by the third of this number you obtain 75. What is the number?
A city square has a rectangular shape of 720 m2. Given that the long is two times the width more 4 metres. What are its measures?
Calculate the width and the height of a pool, given that it is 8m long and the height is two meters less than the width. The pool has a volume of 120 m3.
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