🧮 algebra

1. **State the problem:** Solve the equation $$\frac{a}{x} - \frac{1}{c} = \frac{b}{d}$$ for $x$. 2. **Formula and rules:** To solve for $x$, isolate the term containing $x$ and th

1. **State the problem:** Factor the expression $2mx - 3m + 2pcx - 3pc$ by grouping. 2. **Group terms:** Group the terms to factor common factors:

1. **State the problem:** Solve the equation $$\frac{1}{2}x + 1 = \frac{1}{3}x - 2$$ for $x$. 2. **Formula and rules:** To solve linear equations, we isolate $x$ by moving all term

1. **State the problem:** Divide the polynomial $$-8x^3 - 6x^2 + 15x + 11$$ by the binomial $$2x + 3$$ using long division. 2. **Recall the formula and rules:** Polynomial long div

1. **State the problem:** Calculate $\frac{4}{9}$ times 28. 2. **Formula used:** Multiplying a fraction by a whole number is done by multiplying the numerator by the whole number a

1. The problem is to find the equation of the line passing through the points given in the photo (not provided here). Since the photo is not visible, I will explain the general met

1. The problem involves simplifying the equation $$\frac{96a}{96} + \frac{1392d}{96} = \frac{0}{96}$$ by dividing every term by 96. 2. The formula used here is the property of equa

1. Let's start by understanding the problem: you have an expression after expansion: $$144a - 48a + 2520d - 1128d = 0$$ and you want to verify if this leads to $S_{30} = 870$. 2. F

1. **State the problem:** We have an arithmetic series where the sum of the first 48 terms is 4 times the sum of the first 36 terms. We need to find the sum of the first 30 terms.

1. **State the problem:** Divide the fractions $\frac{1}{8}$ by $\frac{4}{5}$. 2. **Formula:** To divide fractions, multiply the first fraction by the reciprocal of the second frac

1. The problem is to find the sum of the first 194 natural numbers. 2. The formula for the sum of the first $n$ natural numbers is:

1. **State the problem:** We want to find how to get the numbers 2, 42, 47, 57, and 58 from a total sum of 180 using scaling fractions. 2. **Understanding the problem:** Scaling fr

1. **State the problem:** We need to solve the equation step by step. Since no specific equation is given, let's consider a general example: solve for $x$ in the equation $$2x + 3

1. To simplify an expression or solve a problem more simply, always look for common factors or terms that can be combined. 2. Use basic arithmetic operations and properties like di

1. The problem is to explain a math concept suitable for a 14-year-old level. 2. Since no specific problem was given, I will provide a simple algebra example: solving the equation

1. Das Problem lautet: Löse die Gleichung $2x + 3 = 11$.\n\n2. Die allgemeine Formel zum Lösen linearer Gleichungen ist: $ax + b = c \Rightarrow x = \frac{c - b}{a}$.\n\n3. Wende d

1. **Énoncé du problème :** Simplifier la première expression algébrique donnée : $$\frac{2y - 5}{2xy + 2y - 5x - 5}$$

1. The problem asks for the two double inequalities that define the shaded rectangular region on the coordinate plane. 2. The region is bounded by vertical lines at $x = -4$ (dashe

1. The problem asks to write down the two inequalities that define the shaded region on the graph. 2. From the description, the first boundary is a dashed diagonal line passing thr

1. **Restate step 7:** We have the equation from step 6: $$-96a - 1392d = 0$$

1. **State the problem:** We have an arithmetic series where the sum of the first 48 terms is 4 times the sum of the first 36 terms. We need to find the sum of the first 30 terms.