🧮 algebra

1. The problem is to solve the formula $s = \frac{l}{k} t$ for the subject $t$. 2. The formula relates $s$, $l$, $k$, and $t$ with multiplication and division.

1. **State the problem:** Evaluate the expression $16 - 0.5x^5$ when $x = -2$. 2. **Write the formula:** The expression is given as $16 - 0.5x^5$.

1. **State the problem:** Solve the inequality $$|x+1| \le |x-1|$$. 2. **Recall the definition of absolute value:** For any real number $a$, $$|a| = \begin{cases} a & \text{if } a

1. Problem: The sum of two numbers is 26, and their difference is 6. Find the two numbers. Step 1: Define variables. Let the two numbers be $x$ and $y$.

1. **State the problem:** Solve the quadratic equation $$0 = 2x^2 - 14x + 9$$ using the quadratic formula. 2. **Recall the quadratic formula:** For an equation $$ax^2 + bx + c = 0$

1. **Tenglikni isbotlash:** Berilgan tenglik:

1. **State the problem:** Simplify the expression $$\frac{0.25^4 \times 64^2}{2^{-3}}$$. 2. **Rewrite the numbers as powers of 2:**

1. **State the problem:** We have the system of linear equations: $$\begin{cases} 2x - 3y + 4z = 4 \\ 3x + y + 2z = 13 \\ x + 4y - 2z = 9 \end{cases}$$

1. **State the problem:** Simplify the expression $$\frac{0.5^{-4} \times 4^{8}}{32^{5}}$$. 2. **Recall the rules:**

1. **State the problem:** Simplify the expression $$\frac{7^{-1} \times 49^{2}}{343^{-2}}$$. 2. **Recall the base relationships:** Note that 49 and 343 can be expressed as powers o

1. The problem asks for the solution set of an equation in $\mathbb{Q}$ (the set of rational numbers) with options a) 60 b) 150 c) 330 d) 120. However, the equation itself is not p

1. **State the problem:** Simplify the expression $$\frac{2^2 \cdot 2^{-4}}{(2^{-2})^3}$$. 2. **Recall the exponent rules:**

1. Muammo: Berilgan o‘lchamlar bo‘yicha bo‘yalgan yuzni hisoblash formulasini topish. 2. Formulani chiqarish uchun, avvalo, to‘g‘ri to‘rtburchakning yuzini hisoblash formulasi: $$S

1. **State the problem:** Solve the equation $x + 16 = 8 + 10$ for $x$. 2. **Write the equation:**

1. **State the problem:** Determine if each expression is equivalent to $$-0.25y - 0.5$$. 2. **Recall the distributive property:** $$a(b + c) = ab + ac$$. We will apply this to eac

1. The problem asks us to find expressions equivalent to $$\frac{9}{10}x - 2$$. 2. The original expression is $$\frac{9}{10}x - 2$$, which means $$\frac{9}{10}x$$ plus $$-2$$.

1. **State the problem:** We are given the equation of line $f$ as $x + 2y = 16$ and a point $(1, 3)$ through which line $g$ passes. Line $g$ is parallel to line $f$. We need to fi

1. The problem is to rewrite the equation $3x + y = -6$ in slope-intercept form, which is $y = mx + b$, where $m$ is the slope and $b$ is the y-intercept. 2. Start with the given e

1. The problem asks to translate the verbal phrase "One-fourth times a number n, minus thirty" into a mathematical expression. 2. "One-fourth times a number n" means multiply $\fra

1. **State the problem:** We are given the equation of line $g$ as $y = -\frac{1}{3}x - 8$ and a point $(-10, 6)$ through which line $h$ passes. Line $h$ is parallel to line $g$. W

1. The problem is to solve word equations, which means translating words into algebraic expressions or equations and then solving them. 2. The general approach is to identify varia