Mathematics
Grade 9
15 min
Which x satisfies an equation?
Which x satisfies an equation?
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1
Introduction & Learning Objectives
Learning Objectives
Define what it means for a value to 'satisfy' an equation.
Substitute a given value for a variable into a linear or quadratic expression.
Correctly apply the order of operations (PEMDAS/BODMAS) when evaluating expressions.
Determine if a given value is a solution to a linear equation.
Test potential roots to determine if they are solutions to a quadratic equation.
Verify solutions for equations with variables on both sides of the equals sign.
Check if a value satisfies a simple radical equation.
Have you ever tried a key in a lock? 🔑 Some keys fit, but only one will actually turn and open it. How do we find the one 'key' value for x that 'unlocks' an equation?
This tutorial will teach you the fundamental skill of testing...
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Key Concepts & Vocabulary
TermDefinitionExample
EquationA mathematical statement that asserts the equality of two expressions. It always contains an equals sign (=).3x + 5 = 14 is an equation. The expression '3x + 5' is equal to the expression '14'.
VariableA symbol, usually a letter like x or y, that represents an unknown value or a value that can change.In the equation 2x - 7 = 3, 'x' is the variable.
Solution (or Root)A value for a variable that makes an equation true. This is the value that 'satisfies' the equation.For the equation x + 4 = 10, the solution is x = 6 because 6 + 4 = 10 is a true statement.
To Satisfy an EquationWhen a specific value is substituted for the variable in an equation, and the resulting statement is true (i.e., the left side equals the right sid...
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Core Formulas
The Verification Principle
An equation f(x) = g(x) is satisfied by a value x = c if and only if f(c) = g(c).
To check if a number 'c' is a solution, substitute 'c' for every 'x' in the equation. Then, simplify both the left side (LS) and the right side (RS) independently. If the final values are identical (LS = RS), the number is a solution.
Order of Operations (PEMDAS/BODMAS)
1. Parentheses/Brackets, 2. Exponents/Orders, 3. Multiplication and Division (from left to right), 4. Addition and Subtraction (from left to right).
This is the non-negotiable sequence of steps you must follow when simplifying an expression after substituting a value. Following this order ensures you get the correct result.
5 more steps in this tutorial
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Challenging
Which value is a valid solution to the radical equation \(\sqrt{x+7} = x+1\)?
A.x = 2
B.x = -3
C.Both x = 2 and x = -3
D.Neither x = 2 nor x = -3
Challenging
Given that x = -3 is a solution to the equation x² + kx - 21 = 0, what value of k satisfies this condition?
A.k = 7
B.k = -4
C.k = 4
D.k = -7
Challenging
Which value of x satisfies the literal equation 3(x - 2b) = x + 4b?
A.x = 2b
B.x = 4b
C.x = 5b
D.x = b
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