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EXAMPLES & SOLUTIONS
Anchor 1
A one-variable linear equation is an equation that has only one solution.
The symbol sign (=) states that it is an equation.
The expression on one side equals the expression on the other side.
The highest power of an one-variable equation is '1'.
x is often written as 'x'.
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ONE-VARIABLE EQUATION EXAMPLE
Explanation of one-variable equations
equation: x - 3 - 7 = 10, x = ?
Follow properties and PEMDAS:
x - 3 - 7 = 10 --combine & subtract like terms
x - 10 = 10 --updated expression
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.
Follow properties and PEMDAS:
Check:
x - 3 - 7 = 10 --substitute 20 for x
20 - 3 - 7 = 10 --subtraction rule
17 - 7 = 10 --subtraction rule
10 = 10 --CORRECT
One Variable Equation
Examples of an one variable equations
equation: 7 + 3x + 4x = 35
Solve:
7 7
7 + 3x + 4x = 35 --combine & add like terms
7 + 7x = 35
7 - 7 + 7x = 35 - 7 --substract 7 from both sides
0 + 7x = 28
7x = 28 --updated equation
7x = 28 --divide 7 from both sides
x = 28
x = 4
7
--divide rule
Check:
7 + 3x + 4x = 35 --combine & add like terms
7 + 7x = 35 --substitute 4 for x
7 + (7 * 4) = 35 --multiply rule
7 + 28 = 35 --addition rule
35 = 35 --CORRECT
One Variable Equation
Another example of an one variable equations
equation: 5(n + 3) - 1 = 39
Solve:
5(n + 3) - 1 = 39 --distributive property
(5 * n) + (5* 3) - 1 = 39 --multiplication rule
5n + 15 - 1 = 39 --subtraction rule
5n + 14 = 39
5n + 14 - 14 = 39 -14 --subtract 14 from both sides
5n + 0 = 25
5n = 25 --updated equation
5n = 25
x = 5
5 5
--divide 5 from both sides
Check:
5(n + 3) - 1 = 39 --substitute 5 for n
5(5 + 3) - 1 = 39 --distributive property
(5 * 5) + (5 * 3) - 1 = 39 --multiplication rule
25 + 15 - 1 = 39 --addition rule
40 - 1 = 39 --subtraction rule
39 = 39 --CORRECT
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