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Solve for x: 3x + 12 = 5x - 8.
5
10
8
12
10
Use the balance method: Shift the variable with the smaller coefficient to the other side to keep the coefficient positive (5x - 3x = 12 + 8).
A linear equation in one variable: 3x + 12 = 5x - 8.
ax+b=cx+d
Use the balance method: Shift the variable with the smaller coefficient to the other side to keep the coefficient positive (5x - 3x = 12 + 8).
Students often make a sign error when transposing -8 to the left side, accidentally writing it as 12 - 8 instead of 12 + 8.
Group like terms
Collect the variable terms on one side and constant terms on the other side by subtracting 3x from both sides and adding 8 to both sides.
12+8=5xтИТ3x
Simplify both sides
Perform the arithmetic addition and subtraction to simplify the equation into a basic form.
20=2x
Solve for x
Divide both sides of the equation by 2 to isolate the variable x.
x=220тАЛ=10
B is correct because solving the linear equation 3x+12=5xтИТ8 simplifies to 2x=20, which results in x=10.
This concept of isolating variables is foundational for solving quadratic equations and systems of linear equations in coordinate geometry.
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