a) Expand and combine like terms: 9(a - 12) = f) Simplify: (5 - 4(x - 9)) - 40 = b) Expand and combine like terms

Пояснение:
a) To expand and combine like terms in the equation 9(a - 12) = f, we use the distributive property. Multiplying 9 by every term inside the parentheses, we get 9a - 108. Thus, the expanded equation is 9a - 108 = f.

b) Similar to the previous question, we expand and combine like terms in the equation 13 + 2(7 - x). First, we simplify the expression inside the parentheses, which gives us 2(7 - x) = 14 - 2x. Expanding the equation further, we have 13 + 14 - 2x = 27 - 2x.

c) Expanding and combining like terms in the equation 7u - 6(2 + c), we simplify the expression inside the parentheses, resulting in -6c + 4. The expanded equation is 7u - 6c + 4 = c.

d) Expanding and simplifying the equation 121 - (3 + y) 17, we perform the operation inside the parentheses first. 3 + y = y + 3. Then, we multiply (y + 3) by 17 to get 17y + 51. The expanded equation is 121 - 17y - 51 = 0.

e) Expanding and simplifying the equation 25 + 2[12 - 3(x - 7)], we simplify the expression inside the innermost parentheses to get 25 + 2[12 - 3x + 21]. Next, we multiply the terms inside the bracket by 2, which gives us 25 + 24 - 6x + 42. The expanded equation is 49 - 6x = 0.

f) In the equation (5 - 4(x - 9)) - 40, we first simplify the expression inside the parentheses to get 5 - 4x + 36. Then, we combine the like terms to obtain 41 - 4x - 40. The simplified equation is -4x + 1 = 0.

g) Expanding and simplifying the equation {[25x - 3(1 - y)] - 2), we simplify the expression inside the innermost parentheses to get {[25x - 3 + 3y] - 2}. Then, we combine like terms to obtain 25x - 5 + 3y - 2. The expanded equation is 25x + 3y - 7 = 0.

h) Expanding and simplifying the equation {2[5t + 2(15 - 3c)] - k) + 3, we simplify the expression inside the innermost parentheses first, which results in 2[5t + 30 - 6c]. Then, we multiply 2 by each term in the bracket, giving us 10t + 60 - 12c. Further simplifying the equation, we have 10t - 12c - k + 63 = 0.

i) Simplifying the equation [2x - (4 - y)] - 2, we first simplify the expression inside the brackets to get [2x - 4 + y] - 2. Combining like terms, we obtain 2x + y - 6 = 0.

j) In the equation {21 - (5t - 2(5), we first simplify the expression inside the parentheses to get {21 - 5t + 10}. Then we combine like terms to obtain 31 - 5t = 0.

Например: Solve the equation: 25 + 2[12 - 3(x - 7)] = 0.

Совет: When solving equations, it is important to first simplify the expressions inside the parentheses and brackets. Then, combine like terms and apply any necessary operations, such as multiplication and subtraction, to isolate the variable.

Задание для закрепления: Expand and simplify: 16 - 3(4 - 2x) = 8.