🧮 algebra

1. **Stating the problem:** Solve the equation $8g - 7 = 3$ for $g$. 2. **Add 7 to both sides:**

1. The given system of linear equations is: $$3x_1 - 4x_2 - 2x_3 = 2$$

1. The problem is to expand the expression $(x+8)^2$. 2. Recall the formula for expanding a binomial squared: $$(a+b)^2 = a^2 + 2ab + b^2$$.

1. The phrase "rise over run" refers to the slope of a line, which is usually calculated as the ratio of the vertical change (rise) to the horizontal change (run) between two point

1. **State the problem:** Expand the expression $$(x+8)(x-2)$$. 2. **Apply distributive property (FOIL method):** Multiply each term in the first binomial by each term in the secon

1. It seems you asked, "How did you simplify?" but did not provide a specific expression or problem to simplify. 2. To assist you effectively, please provide the exact algebraic ex

1. **Stating the problem:** The first three terms of an arithmetic progression (A.P) are given as $2x$, $(3x - 1)$, and $(x + 4)$. We need to find: i. The value of $x$

1. Problem: The sum of the first 10 terms of an arithmetic progression (A.P.) is 240 and the 8th term is 34. a. Find the common difference.

1. The user asked about the variable "a" which was not mentioned previously. 2. Without specific context, "a" can represent a constant, coefficient, or variable in an equation.

1. The problem asks to convert the fraction $\frac{8}{20}$ to a percentage. 2. To convert a fraction to a percentage, divide the numerator by the denominator and then multiply by 1

1. **Stating the problem:** Add the two very large numbers: $$1000000000000000000000000 + 9179274828672936491973829264839274820384728946190275728374728$$. 2. **Write the numbers cl

1. The problem asks us to find the value of each interval on two number lines using the formula: Difference between the start and end points \div the number of intervals

1. The problem asks to find the square root of 144. 2. The square root of a number $x$ is a number $y$ such that $y^2 = x$.

1. Let's start by stating the problem: Solve for $d$ in the equation $$68 - 14d + 9d = 48$$. 2. Combine like terms involving $d$: $$-14d + 9d = -5d$$, so the equation becomes $$68

1. The problem is to simplify the expression $$3^3 t^4 \div 3^2 t^2$$. 2. We can rewrite the division as the multiplication by the reciprocal:

1. **State the problem:** The principal amount becomes 5 times in 12 years. We want to find how many times the principal will become in 27 years. 2. **Understand the problem:** The

1. The problem is to evaluate the expression $5(17)2 / 103$. 2. First, calculate the multiplication inside the numerator: $5 \times 17 \times 2$.

1. Stating the problem: Simplify the expression $$3^2 \times 6 \times 4 \div 3 \times 2 \times 6 \times 2$$. 2. First, evaluate the exponent: $$3^2 = 9$$.

1. **State the problem:** We are given the sum of the first 10 terms of an arithmetic progression (A.P.) as 240 and the 8th term as 34. We need to find the common difference $d$ of

1. State the problem: Solve the exponential equation $$12^{x-2} = 3^{3x} \cdot 2^{6x}$$ for $x$. 2. Express all terms with prime factors: Note that $12 = 2^2 \cdot 3$, so $$12^{x-2

**المعيار: حل المعادلات باستخدام المعاملات النسبية** 1. حل المعادلة $\frac{1}{2} y = 3 \frac{3}{10}$