🧮 algebra

1. **State the problem:** Simplify the expression $x + 3 + x - 1$. 2. **Combine like terms:** Group the $x$ terms and the constant terms separately.

1. The problem states that the marked price (m.p) of an item is 850 and there is a discount of 5%.\n\n2. To find the discount amount, calculate 5% of 850 using the formula: $$\text

1. The expression given is $9b$. 2. This represents the product of the number 9 and the variable $b$.

1. **Problem 9a:** Write down the first four and last two terms of the binomial expansion of $ (2 + x)^n $ where $ n \in \mathbb{Z}^+ $. The binomial expansion formula is:

1. The problem is to express 144 as a product of its prime factors. 2. Start by dividing 144 by the smallest prime number 2: $$144 \div 2 = 72$$.

1. **State the problem:** We have a sequence where each term is obtained by adding 4 to the previous term and then dividing by 2. 2. **Given terms:** The sequence is \(a_1, 6, 5, 4

1. **State the problem:** We have a sequence where each term is found by multiplying the previous term by 4 and then subtracting 34. 2. **Given:** The 12th term, $a_{12} = 25$.

1. The problem gives a sequence with some missing terms and a term-to-term rule: subtract 12. 2. The known terms are the 2nd term = 23 and the 3rd term = 11.

1. المشكلة: لدينا معادلتان خطيتان تمثلان مجموع عددين $x$ و $y$، حيث: $$x + y = 12$$

1. **State the problem:** Simplify the expression $$725 - [20 \times \{10 + 7 + (7 \times 5 - 3)\}]$$. 2. **Calculate inside the parentheses:**

1. **Problem:** Find the ratio of cats to fish given dogs:cats = 5:3 and fish:dogs = 6:1. Step 1: Express dogs, cats, and fish in terms of a common variable.

1. Let's start by stating the problem: factoring polynomials means expressing a polynomial as a product of simpler polynomials. 2. For example, consider the polynomial $x^2 - 5x +

1. **State the problem:** We have a rectangle with sides labeled as $2x$ (vertical side) and $3 \times 3$ (horizontal side). The perimeter is given as 14 units. We need to find the

1. समस्या को समझें: A और B मिलकर एक कार्य 12 दिन में पूरा करते हैं। B अकेले वह कार्य 10 दिन में करता है। हमें यह पता लगाना है कि A अकेले वह कार्य कितने दिन में पूरा करेगा। 2. कार्य

1. The problem is to simplify the expression $$\frac{72y}{88}$$. 2. First, find the greatest common divisor (GCD) of 72 and 88 to simplify the fraction.

1. **State the problem:** Solve the inequality $5(x - 4) < 3(2x - 1)$ and find the solution set for $x$. 2. **Expand both sides:**

1. **State the problem:** Solve the inequality $$5(x - 4) < 3(2x - 1)$$. 2. **Expand both sides:**

1. **State the problem:** Solve the inequality $$3(x + 4) - 5 > -3(x - 2) + 13$$ and determine the correct graph representing the solution. 2. **Expand both sides:**

1. **State the problem:** Solve the inequality $$3(x + 4) - 5 > -3(x - 2) + 13$$. 2. **Expand both sides:**

1. We are given the inequality $$\frac{2x + 2}{6} - \frac{3x - 1}{11} \leq -5$$ and need to solve for $x$. 2. First, find a common denominator to combine the fractions on the left

1. **State the problem:** Solve the inequality $$\frac{2x+2}{6} - \frac{3x-1}{11} \leq -5$$ and determine which option (A, B, C, or D) correctly represents the solution for $x$. 2.