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EXAMPLES & SOLUTIONS
Anchor 1
A mathematical equation in which two expressions are not equal to each other.
This states that the expression on one side may not equal the expression on the other side.
Many x-values can be substituted to make the equation correct.
The possible symbol signs for the equation are >, <, > , <.
If the operators <, > are utilized then one side is not equal to the other side.
Operators < , > have one side that is not equal to each other. If they are equal, then they are only being compared.
INEQUALITY EQUATIONS
Explanation of equations with inequalities
inequality: x - 3 - 7 < 10, x = ?
Solve:
Follow properties and PEMDAS:
x - 3 - 7 < 10 --combine & subtract like terms
x -10 < 10 --updated inequality
x - 10 + 10 < 10 + 10 --add 10 to both sides
x + 0 < 20
x < 20
Fact: It is always good to verify (check) your answer.
Check:
Follow properties and PEMDAS:
x - 3 - 7 < 10 --original problem
x - 10 < 10 --combine terms
3 - 10 < 10 --substitute any number x < 20, x = 3 -7 < 10 --CORRECT
Inequality Equations
Example of inequality equations
equation: 7 + 3x - 4x < 35
Solve:
7 + 3x + 4x < 35 --combine & add like terms
7 + 7x < 35
7 - 7 + 7x < 35 - 7 --subtract 7 from both sides
0 + 7x < 28
7x < 28 --updated equation
7x < 28 --divide 7 from both sides
x < 4
7 7
Check:
7 + 3x + 4x < 35 --substitute any value < 4; x = 4
7 + 3(4) + 4(4) < 35 --multiply rule
7 + 12 + 16 < 35 --addition rule
35 < 35 --CORRECT
Check:
7 + 3x + 4x < 35 --substitute any value < 4; x = 2
7 + 3(2) + 4(2) < 35 --multiply rule
7 + 6 + 8 < 35 --addition rule
21 < 35 --CORRECT
Inequality Equations
Another example of inequality equations
equation: -3n - 1 > 8
Solve:
-3n - 1 > 8
-3n -1 + 1 > 8 + 1 --subtract rule
-3n + 0 > 9 --updated expression
-3n > 9 --subtract 6 from both sides
-3n > 9
n < -3
-3 -3
--divide 3 from both sides
--switch signs
Check:
-3n - 1 > 8 --substitute any value < -3, n = -3
-3(-3) - 1 > 8 --multiply rule
9 - 1 > 8 --subtraction rule
8 > 8 --CORRECT
Check:
-3n - 1 > 8 --substitute any value < -3, n = -6
-3(-6) - 1 > 8 --multiply rule
18 - 1 > 8 --subtraction rule
17 > 8 --CORRECT
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