76 Algebra (Equations and inequalities) (Chapter 3)SIDES OF AN EQUATION
Theleft hand side(LHS) of an equation is on the left of the=sign.
Theright hand side(RHS) of an equation is on the right of the=sign.For example, (^3) |x{z+7}
LHS
=13|{z}
RHS
THE SOLUTIONS OF AN EQUATION
Thesolutionsof an equation are the values of the variable which make the equation true,
i.e., make theleft hand side (LHS)equal to theright hand side (RHS).
In the example 3 x+7=13 above, the only value of the variablexwhich makes the equation true is
x=2.
Notice that when x=2, LHS=3x+7
=3£2+7
=6+7
=13
=RHS ) LHS=RHS
MAINTAINING BALANCE
Thebalanceof an equation is maintained provided we perform the same operation onboth sidesof the
equals sign. We can compare equations to a set of scales.
Adding to, subtracting from, multiplying by, and dividing by the same quantity onboth sidesof an equation
willmaintain the balanceorequality.
When we use the “=” sign between two algebraic expressions we have an equation which is in balance.
Whatever we do to one side of the equation, we must do the same to the other side tomaintain the balance.
Compare the balance of weights:
We perform operations on both sides of each equation in order toisolate the unknown. We consider how
the expression has beenbuilt upand thenisolate the unknownby usinginverse operationsinreverse
order.
x 2 x 2 x+3
For example, for the equation 2 x+3=8, the LHS is built up
by starting withx, multiplying by 2 , then adding 3.
So, to isolatex, we first subtract 3 from both sides, then divide
both sides by 2.
add 2
remove 3
from both sides
2 +3=8x \2=5x
£ 2
¥ 2
+3
¡ 3
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Y:\HAESE\IGCSE01\IG01_03\076IGCSE01_03.CDR Friday, 12 September 2008 12:04:05 PM PETER