Consider the equation ax + b = c. First subtract b from
both sides to get ax + b - b= c - b.
Dividing both sides by a, x = (c - b)/a.
Example
Let us solve a linear equation . Consider 3x + 5 = 11.
Subtracting 5 from both sides of equation, 3x
+ 5 - 5 = 11 - 5 which implies 3x = 6. Dividing both sides of the equation by 3,
3x/3 = 6/3 which
leads to x = 2. Thus the solution to the given equation is 2. Intuitively, this
means that the only
number that would make the LHS and the RHS equal to each other is the number 2.
Application
Jeff spends his al lowance on erasers and pencils. This
week Jeff bought 4 erasers that were priced
at 50 cents apiece. If Jeff’s allowance is $5 per week, and he always spends his
entire allowance,
find out how many pencils he bought if they cost $1 each.
Jeff’s weekly budget equation can ex pressed as p * n + e *
m = A where p and e are the prices of
pencils and erasers respectively, n and m are the numbers of pencils and erasers
he buys and A
represents his weekly allowance. Putting in numbers for p, e, m and A,1 * n +
0.50 * 4 = 5 . This
can be rewritten as n + 2 = 5 which leads to the solution n = 3. Therefore, Jeff
bought 3 pencils
this week.
