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How to Solve the One-Variable Linear Equation 3x + 7 = 22
Mathematics
Grade 7
Question Content
Solve for x: 3x + 7 = 22
Correct Answer
x = 5
Detailed Solution Steps
1
Step 1: Isolate the term with the variable by subtracting 7 from both sides of the equation to maintain equality: 3x + 7 - 7 = 22 - 7, which simplifies to 3x = 15.
2
Step 2: Solve for x by dividing both sides of the equation by the coefficient of x, which is 3: 3x ÷ 3 = 15 ÷ 3, which simplifies to x = 5.
3
Step 3 (Verification): Substitute x = 5 back into the original equation: 3(5) + 7 = 15 + 7 = 22, which matches the right-hand side, confirming the solution is correct.
Knowledge Points Involved
1
One-variable linear equation definition
A one-variable linear equation is an algebraic equation that contains only one variable, where the highest power of the variable is 1, following the standard form ax + b = 0 (a ≠ 0). It represents a straight line when graphed, and has exactly one real solution.
2
Properties of equality
The properties state that if the same number is added, subtracted, multiplied, or divided (by a non-zero number) to both sides of an equation, the equality remains true. This is the core rule used to isolate the variable and solve the equation.
3
Isolating the variable in linear equations
This is a problem-solving method where inverse operations are used to move all constant terms to one side of the equation and the variable term to the other, then solve for the variable by dividing by its coefficient. It is the standard approach for solving one-variable linear equations.
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