🧮 algebra

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.

1. Let's clarify the question: "Is Z negative?" This depends on the context or the definition of Z in your problem. 2. If Z is a variable or a value, you need to check its value or

1. **Problem statement:** We are given the function $$f(x) = \frac{x^3 - 16x}{-4x^2 + 4x + 24}$$ and asked to analyze it, including graphing the curve and its asymptotes. 2. **Simp

1. **Problem statement:** We are given the function $$f(x) = \frac{x^3 - 16x}{-4x^2 + 4x + 24}$$ and asked to analyze and graph it, including its oblique (slant) asymptotes. 2. **S

1. **State the problem:** Simplify the expression $$\frac{x^4 - y^4}{x^2 - 2xy + y^2} \times \frac{x - y}{x(x + y)} \div \frac{x^2 + y^2}{x}$$. 2. **Rewrite the division as multipl

1. **Expand** $(x + 2)^4$ using the binomial theorem. The binomial theorem states:

1. The problem asks to solve the equations graphically: 10. $|x - 1| = 2$

1. The problem is to understand the expression $\frac{a}{b}$, which represents a fraction where $a$ is the numerator and $b$ is the denominator. 2. This fraction means that $a$ is

1. The problem gives two equations: $y=3m+4$ and $x=5m-6$. 2. These equations express $y$ and $x$ in terms of the parameter $m$.

1. **Check the consistency and solve the system:** Given:

1. **State the problem:** We have the cryptarithm (alphametic puzzle): $$\begin{array}{cccc}

1. The problem is to find the expression for $2 \times A$ where $A$ is a variable or a given quantity. 2. Multiplying a variable by 2 means doubling its value.

1. Problem: Find the inverse function $f^{-1}(x)$ for $f(x) = \frac{2x+1}{x-1}$, $x>1$. 2. To find $f^{-1}(x)$, start by setting $y = \frac{2x+1}{x-1}$.