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Solve Linear Equation \( 5x - 3 = 2x + 9 \) for \( x \)
Mathematics
Middle School (Grade 7-8)
Question Content
Solve for \( x \): \( 5x - 3 = 2x + 9 \)
Correct Answer
\( x = 4 \)
Detailed Solution Steps
1
Step 1: Subtract \( 2x \) from both sides to eliminate \( 2x \) on the right: \( 5x - 2x - 3 = 2x - 2x + 9 \), simplifying to \( 3x - 3 = 9 \).
2
Step 2: Add \( 3 \) to both sides to isolate the term with \( x \): \( 3x - 3 + 3 = 9 + 3 \), simplifying to \( 3x = 12 \).
3
Step 3: Divide both sides by \( 3 \): \( \frac{3x}{3} = \frac{12}{3} \), resulting in \( x = 4 \).
Knowledge Points Involved
1
Linear Equations in One Variable
Equations of the form \( ax + b = cx + d \) (where \( a, b, c, d \) are constants) solved by isolating the variable \( x \) using properties of equality.
2
Properties of Equality
Adding/subtracting the same quantity to both sides, or multiplying/dividing both sides by a non - zero quantity, preserves the equality of the equation.
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