Solve for x: 3x + 5 = 2x + 11.

Solve for x: 3x + 5 = 2x + 11.

• A. 2
• B. 6
• C. 11
• D. -6

Answer: (B)

Solving a linear equation by isolating the variable. First get all x terms on one side: subtract 2x from both sides to obtain x + 5 = 11. Then remove the constant term by subtracting 5 from both sides, giving x = 6. This satisfies the equation, since 3(6) + 5 = 18 + 5 = 23 and 2(6) + 11 = 12 + 11 = 23. Other candidate values don’t balance the two sides (for example, x = 2 gives 11 on the left and 15 on the right; x = 11 gives 38 on the left and 33 on the right; x = -6 gives -13 on the left and -1 on the right).

Solving a linear equation by isolating the variable. First get all x terms on one side: subtract 2x from both sides to obtain x + 5 = 11. Then remove the constant term by subtracting 5 from both sides, giving x = 6. This satisfies the equation, since 3(6) + 5 = 18 + 5 = 23 and 2(6) + 11 = 12 + 11 = 23. Other candidate values don’t balance the two sides (for example, x = 2 gives 11 on the left and 15 on the right; x = 11 gives 38 on the left and 33 on the right; x = -6 gives -13 on the left and -1 on the right).