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How to Solve the One-Variable Linear Equation -9x + 6 = 78
Mathematics
Grade 7 (Junior High School)
Question Content
Solve the linear equation: -9x + 6 = 78
Correct Answer
x = -8
Detailed Solution Steps
1
Step 1: Isolate the term with the variable by subtracting 6 from both sides of the equation to maintain equality: -9x + 6 - 6 = 78 - 6, which simplifies to -9x = 72
2
Step 2: Solve for x by dividing both sides of the equation by -9: (-9x) ÷ (-9) = 72 ÷ (-9)
3
Step 3: Calculate the result to get x = -8
Knowledge Points Involved
1
One-variable linear equation definition
A one-variable linear equation is an algebraic equation that contains only one variable, and the highest power of the variable is 1, with the general form ax + b = 0 (a ≠ 0). It is the basic type of equation learned in early junior high school, used to solve practical and abstract quantitative relationship problems.
2
Properties of equality
1. If the same number (or algebraic expression) is added or subtracted from both sides of an equation, the equality still holds. 2. If both sides of an equation are multiplied or divided by the same non-zero number, the equality still holds. These properties are the core basis for solving equations, used to transform equations to isolate the variable.
3
Solving steps for one-variable linear equations
The general steps are: 1. Remove parentheses (if any); 2. Move terms (move terms with variables to one side and constant terms to the other); 3. Combine like terms; 4. Convert the coefficient of the variable to 1. For this problem, we only need to use the property of equality to isolate the variable term first, then convert the coefficient to 1.
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