We need to solve $12 + 0.75x = 0.5x + 18$ for the number of gigabytes $x$. Subtracting $0.5x$ from both sides: $12 + 0.75x - 0.5x = 18$, which simplifies to $12 + 0.25x = 18$. Subtracting 12 from both sides: $0.25x = 6$. Dividing by 0.25: $x = 6 ÷ 0.25 = 24$. A common error is making arithmetic mistakes with decimals or incorrectly combining the $x$ terms. When working with decimal coefficients, consider converting to fractions to avoid calculation errors.

This problem asks us to find the monthly fee $x$ when the total cost after 6 months equals $18 + 6x = 3x + 54$. To solve, we first subtract $3x$ from both sides: $18 + 6x - 3x = 54$, which simplifies to $18 + 3x = 54$. Next, we subtract 18 from both sides: $3x = 54 - 18 = 36$. Finally, dividing both sides by 3 gives us $x = 12$. A common error is incorrectly combining the $x$ terms or making arithmetic mistakes when subtracting. When solving equations with variables on both sides, always collect like terms on one side first.

The problem asks to find x from the phone plan equation $18 + 7x = 46$, where 18 is the base charge and $7x$ represents 7 gigabytes at x dollars each. Subtract 18 from both sides: $7x = 46 - 18 = 28$. Divide both sides by 7: $x = 28 \div 7 = 4$. A common mistake would be dividing the wrong terms or making arithmetic errors in subtraction. Always isolate the variable term first, then divide by its coefficient.

The problem describes a streaming service billing equation 9 + 5x = 24, where 9 is the base fee and 5x represents 5 movies at x dollars each. Subtract 9 from both sides: 5x = 15, then divide by 5: x = 3. A common mistake would be dividing by the wrong coefficient or making arithmetic errors in subtraction. When solving real-world problems, identify the fixed and variable costs before isolating the variable.

The problem asks to solve 5x + 12 = 3x - 8 for x, which has variables on both sides. Subtract 3x from both sides: 2x + 12 = -8. Subtract 12 from both sides: 2x = -20. Divide both sides by 2: x = -10. A key mistake would be incorrectly moving terms or making sign errors when combining like terms. When variables appear on both sides, collect all variable terms on one side and constants on the other.

The problem asks to solve (2x - 1)/3 = (x + 5)/2 for x. Cross-multiply to get 2(2x - 1) = 3(x + 5), which gives 4x - 2 = 3x + 15. Subtract 3x from both sides: x - 2 = 15, then add 2: x = 17. A common error is making mistakes during cross-multiplication or not properly distributing. When solving rational equations, cross-multiplication is often the most efficient method to eliminate fractions.

The problem describes a water tank draining equation 120 - 9x = 66, where 120 is initial volume, 9x is amount drained in 9 minutes at x liters per minute, and 66 is final volume. Subtract 120 from 66: -9x = 66 - 120 = -54. Divide by -9: x = 6. A common mistake would be incorrect subtraction or sign handling. When solving real-world problems, ensure the equation makes physical sense before solving.

The problem describes a class collection equation 30 + 10x = 180, where 30 is a fixed fee and 10x represents 10 students at x dollars each. Subtract 30 from both sides: 10x = 150, then divide by 10: x = 15. A common mistake would be dividing by the wrong coefficient or making subtraction errors. When solving real-world problems, identify the fixed and variable components clearly before isolating the variable.

The problem asks to solve the taxi fare equation 3.50 + 2.25x = 21.50 for x, where x represents miles traveled. Subtract 3.50 from both sides: 2.25x = 18. Divide both sides by 2.25: x = 18 ÷ 2.25 = 8. A common error would be incorrect decimal division or forgetting to subtract the base fare first. When solving real-world linear equations, identify the fixed cost and variable cost components before isolating the variable.

The problem describes a contractor's billing equation $50 + 3x = 170$, where 50 is the visit fee and $3x$ represents 3 hours at x dollars per hour. Subtract 50 from both sides: $3x = 120$, then divide by 3: $x = 40$. A common mistake would be dividing by the wrong coefficient or making subtraction errors. When solving real-world linear equations, clearly identify the fixed and variable components before isolating the variable.