🧮 algebra

1. **State the problem:** A father's age is 4 times that of his elder son and 5 times that of his younger son. When the elder son has lived three times his present age, the father'

1. **State the problem:** Solve the inequality $x^2 - 1 \le 0$. 2. **Recall the formula and rules:** This is a quadratic inequality. We can factor the quadratic expression and anal

1. **State the problem:** Solve the inequality $1 - x^2 \ge 0$. 2. **Recall the formula and rules:** This is a quadratic inequality. We want to find values of $x$ such that $1 - x^

1. Let's start by understanding what you need help with. Since you mentioned examples and practice questions, I'll provide a general approach to solving algebra problems with examp

1. **State the problem:** Simplify the expression $5 - 3(8)$. 2. **Recall the order of operations:** According to the order of operations (PEMDAS/BODMAS), multiplication is perform

1. Bài tập đề xuất liên quan đến dạng toán này thường là giải phương trình, rút gọn biểu thức, hoặc tìm nghiệm của đa thức. 2. Ví dụ bài tập: Giải phương trình $$2x^2 - 5x + 3 = 0$

1. **Stating the problem:** We need to find which of the given expressions (a) to (f) are equal to which of the expressions A) to F) by expanding and simplifying the products of bi

1. The problem states that the function domain is $0 \leq x \leq 4$, meaning $x$ can take any value from 0 to 4 inclusive. 2. This defines a horizontal line segment on the number l

1. The problem states the constraint on the variable $x$ as $0 \leq x \leq h$. 2. This means $x$ can take any value starting from 0 up to and including $h$.

1. **Stating the problem:** We want to understand the different types of surds in mathematics. 2. **Definition:** A surd is an irrational root of a number that cannot be simplified

1. The problem states the domain of the variable $x$ as $-1 \leq x \leq 3$. 2. This means $x$ can take any value starting from $-1$ up to $3$, including both endpoints.

1. The problem asks about the nature of $\sqrt{n}$ when $n$ is not a perfect square. 2. A perfect square is an integer that can be expressed as $k^2$ where $k$ is an integer.

1. **Problem Statement:** Write the general equation of a circle with center at (2, 6) and radius 9 units, then find values of D, E, and F. 2. **Formula:** The standard form of a c

1. The problem states the inequality $-2 \leq x \leq 5$, which means $x$ is a number between $-2$ and $5$, including both endpoints. 2. This is a compound inequality representing t

1. Calculate 80% of 20. Formula: $\text{Percentage value} = \frac{\text{Percentage}}{100} \times \text{Total}$

1. **Problem statement:** Given points P(-3,4), M(a,2) which is the midpoint of PQ, and Q lies on the x-axis (so Q's y-coordinate is 0). We need to find: 2.1 The gradient of PQ.

1. **Stating the problem:** Solve the simultaneous equations: $$4x - 5y = 13$$

1. **Problem Statement:** We are given points $P(-3,4)$ and $Q$ lies on the positive x-axis. We need to determine the gradient (slope) of the line segment $PQ$. 2. **Understanding

1. Problem: Solve the inequality $$\frac{3x}{2-x} \leq 3$$ Step 1: Write the inequality clearly.

1. **Solve the inequality** $$\frac{3x}{2 - x} \leq 3$$ - Multiply both sides by the denominator, considering the sign of $$2 - x$$.

1. **Stating the problem:** We need to solve the expression: $50 \times 20 \times 30 \times 40 \times 50 - - - - - - \times 1000$.