The question asks for the value of s when f=4 in the equation 2f + s = 11. This is a linear equation with two variables, constraining the amounts of flour f and sugar s. Substitute f=4: 24 + s = 11, which is 8 + s = 11. Then, subtract 8 from both sides: s = 11 - 8 = 3. A common error is to multiply instead of adding or solving for f instead. Verify by plugging back: 24 + 3 = 8+3=11, correct. When given a value for one variable, substitute directly to find the other in two-variable equations.

This problem asks to solve 5x + y = 3 for y. Subtracting 5x from both sides: y = 3 - 5x. This can also be written as y = -5x + 3, but the form y = 3 - 5x matches choice B exactly. The equation shows that y decreases by 5 units for each unit increase in x. A common error is making sign errors when moving terms across the equal sign. When isolating variables, perform the same operation to both sides systematically.

The question asks for the value of y when x=6 in the equation 5x - 2y = 14. This is a linear equation in two variables. Substitute x=6: 56 - 2y = 14, which is 30 - 2y = 14. Subtract 30 from both sides: -2y = 14 - 30 = -16. Divide by -2: y = -16 / -2 = 8. A common error is sign mistakes when dividing by negative numbers or incorrect substitution. Verify: 56 - 2*8 = 30 - 16 = 14, yes. In solving, carefully handle negative signs and isolate the variable step by step.

The question asks for the equation that solves for n in terms of T and s, given T = 4n + s. This equation models the total cost T as 4 times the price per notebook n plus shipping s. To solve for n, subtract s from both sides: T - s = 4n. Then, divide both sides by 4: n = (T - s)/4. A common error is to divide by something else or forget to subtract s first. Check by substituting back; if T=20, s=4, n=4, then 20=4*4 +4, yes, and (20-4)/4=4. Focus on inverse operations to isolate the desired variable in equations with multiple variables.

This problem gives y = (-3/4)x + 6 and asks for y when x = 8. Substituting x = 8: y = (-3/4)(8) + 6 = -6 + 6 = 0. The calculation involves multiplying the fraction by 8: (-3/4) × 8 = -3 × 2 = -6, then adding 6 gives 0. A common error is making mistakes with fraction arithmetic or sign errors. When evaluating linear expressions with fractions, multiply carefully and follow the order of operations.

The question asks how sugar s changes when flour f increases by 8 cups, given s = (3/4)f. When f increases by 8, the new sugar amount is s_new = (3/4)(f + 8) = (3/4)f + (3/4)(8) = (3/4)f + 6. The change in sugar is s_new - s = (3/4)f + 6 - (3/4)f = 6 cups. The key insight is that for proportional relationships, the change in one variable equals the constant of proportionality times the change in the other variable: (3/4) × 8 = 6. Avoid the error of thinking the change depends on the initial value of f.

This question asks how the total cost C changes when the number of months m increases by 4. The cost function is C = 25 + 18m, where 25 is the one-time sign-up fee and 18 is the monthly fee. When m increases by 4, the new cost becomes C_new = 25 + 18(m + 4) = 25 + 18m + 72. The change in cost is C_new - C = (25 + 18m + 72) - (25 + 18m) = 72 dollars. A common error is to only multiply the increase in months by the coefficient without considering the constant term, but since the constant 25 appears in both expressions, it cancels out. When dealing with linear functions, the change in output equals the rate of change times the change in input.

The question asks us to solve for d in terms of F from the equation F = 3.50 + 2.25d. To isolate d, first subtract 3.50 from both sides: F - 3.50 = 2.25d. Then divide both sides by 2.25 to get d = (F - 3.50)/2.25. This matches answer choice B. A common mistake is to incorrectly rearrange the equation by dividing before subtracting or confusing which term to subtract. When solving for a variable, perform inverse operations in reverse order: first undo addition/subtraction, then undo multiplication/division.

This question asks for an equation representing total cost C after m months with a monthly fee of p dollars and a one-time activation fee of 40 dollars. The total cost equals the monthly fee times the number of months plus the one-time fee: C = pm + 40. This matches answer choice C. Common errors include adding all three variables (C = 40 + m + p) or creating nonsensical operations like division. When modeling costs with recurring and one-time fees, multiply the recurring fee by the time period and add any fixed fees.

This problem involves y = (5/2)x - 1, where if x increases by 4, we need to find how y changes. The change in y equals the coefficient of x times the change in x: Δy = (5/2) × 4 = 5 × 2 = 10. The coefficient 5/2 represents the slope or rate of change. When x increases by 4, y increases by 10. A common error is making mistakes with fraction arithmetic or forgetting to multiply by the coefficient. In linear relationships, changes in the dependent variable equal the slope times changes in the independent variable.