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Solve for x: 3x + 15 = 45 - 2x
5
6
8
10
6
Plug the options into the equation: for option B, 3(6) + 15 = 18 + 15 = 33, and 45 - 2(6) = 45 - 12 = 33. Since both sides match, 6 is the correct answer.
A linear equation in one variable: 3x + 15 = 45 - 2x
ax+b=c−dx⟹x=a+dc−b
Plug the options into the equation: for option B, 3(6) + 15 = 18 + 15 = 33, and 45 - 2(6) = 45 - 12 = 33. Since both sides match, 6 is the correct answer.
Students often make a sign error when moving -2x to the left side or 15 to the right side of the equation.
Group like terms
Collect the variable terms on the left and the constant terms on the right side of the equation.
3x+2x=45−15
Simplify both sides
Perform the addition and subtraction for each side of the equation.
5x=30
Solve for x
Divide both sides by the coefficient of x, which is 5.
x=530=6
B is correct because solving the linear equation 3x + 15 = 45 - 2x yields the value x = 6.
This concept of isolating variables is the foundation for solving complex algebraic expressions, quadratic equations, and coordinate geometry problems.
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