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A non-linear equation does not form a straight line. It can have rational or irrational numbers in the equations.
The symbol sign (=) states that it is an equation.
It can have rational or irrational numbers in its' equation.
It can have degrees of 2 or more.
It is never straight, but always curved in someway.
NON-LINEAR EQUATION
Explanation of equations that are non-linear
equation: x - 3 - 7 = 15, x = ?
2
Solve:
Follow properties and PEMDAS:
2
x - 3 - 7 = 15 --combine terms & substract
x - 10 = 15 --updated expression
x - 10 + 10 = 15 + 10 --add 10 to both sides
x + 0 = 25 --square each side
x = 25
x = + 5
2
2
2
2
Fact: It is always good to verify (check) your answer.
Check:
Follow properties and PEMDAS:
x - 3 - 7 = ? --substitute 5 for x (answer)
5 - 10 = 15 --exponent rule
(5 * 5) - 10 = 15 --multiply
25 - 10 = 15 --subtract rule
15 = 15 --CORRECT
2
2
x - 3 - 7 = ? --substitute -5 for x (answer)
-5 - 10 = 15 --exponent rule
(-5 * -5) - 10 = 15 --multiply
25 - 10 = 15 --subtract rule
15 = 15 --CORRECT
2
2
Non-Linear Equations
Examples of equations that are non-linear with even exponent
expression: 11 + 2x + 4x = 35, x = ?
2
2
Solve:
6 6
2
2
2
2
11 + 2x + 4x = 35 --exponent rule
11 + 6x = 35 --add coefficient, keep base
11 - 11 + 6x = 35 -11 --subtract -11 from both sides
0 + 6x = 24
6x = 24 --updated equation
6x = 24 --divide 6 from both sides
x = 4
x = + 2
2
2
2
2
expression: 11 + 2x + 4x = 35, x = ?
2
2
Check:
2
2
11 + 2(2) + 4(2) = 35 --substitute 2 for x
11 + 2(2 * 2) + 4 (2 * 2) = 35 --exponent rule
11 + 2(4 )+ 4(4) = 35 --multiple rule
11 + 8 + 16 = 35 --subtract 7 from both sides
35 = 35 --CORRECT
expression: 11 + 2x + 4x = 35, x = ?
2
2
Check:
2
2
11 + 2(-2) + 4(-2) = 35 --substitute -2 for x
11 + 2(-2 * -2) + 4 (-2 * -2) = 35 --exponent rule
11 + 2(4 )+ 4(4) = 35 --multiple rule
11 + 8 + 16 = 35 --subtract 7 from both sides
35 = 35 --CORRECT
Non-Linear Equations
Examples of equations that are non-linear with odd exponents
Solve:
3
equation: n - 18 = 27, n = ?
3
n
3
27
=
3
n - 18 = 9
n + 18 - 18 = 9 + 18 --subtract 2 from both sides
n + 0 = 27 --updated equation
n = 3
3
3
Check:
3
expression: n + 2 = -6, n = 3
n - 18 = 9
3 - 18 = 9 --substitute 2 for x
3 - 18 = 9 --subtract 2 from both sides
( 3 * 3 * 3) - 18 = 9
27 - 18 = 9 --CORRECT
3
3
3
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