🧮 algebra

1. **State the problem:** Solve the inequality $-26 + 4y > 2$ for $y$. 2. **Add 26 to both sides:**

1. **State the problem:** Solve the inequality $-26 + 4y > 2$ for $y$. 2. **Write the inequality:**

1. **Problem statement:** Berechne die fehlenden Koordinaten der Punkte A, A' und C, C' sowie die fehlenden Komponenten der Vektoren \(\vec{v}^*\).

1. **State the problem:** Solve the inequality $5(2h + 8) < 60$. 2. **Use the distributive property:** Multiply 5 by each term inside the parentheses.

1. **State the problem:** Simplify the expression $$\frac{-28a^{16}b^{8}c^{5}}{7a^{11}b^{5}c^{5}}$$. 2. **Recall the rules:**

1. The problem is to evaluate the expression $2^{-5}$.\n\n2. Recall the rule for negative exponents: $a^{-n} = \frac{1}{a^n}$ where $a \neq 0$ and $n$ is a positive integer.\n\n3.

1. **State the problem:** Factorise the expression $pm + 3p - m - 3$. 2. **Recall the factoring method:** We can use grouping to factorise expressions with four terms. Group terms

1. **State the problem:** Find the range of values of $t \in \mathbb{R}$ such that the point $(5,t)$ lies inside the circle defined by $$(x-3)^2 + (y+2)^2 = 29.$$\n\n2. **Recall th

1. The problem asks to create tables of values for each linear relation for $x = 0, -1, -2, -3, -4$ and then graph the lines. 2. The general form of a linear equation is $y = mx +

1. Le problème est de résoudre l'inéquation $$\frac{2x - 1}{1 - 4x} > 0$$. 2. Pour résoudre une inéquation de type fraction, on étudie le signe du numérateur et du dénominateur.

1. **State the problem:** We are given the quadratic expression $$2x^2 - 6x - 20$$ and asked to fill in the gaps in the expression $$2x^2 - 6x - 20 = \square (x^2 - \square x - \sq

1. **State the problem:** Solve for $h$ in the equation $$\frac{h}{3} - 1 = 1.$$\n\n2. **Add 1 to both sides:** To isolate the term with $h$, add 1 to both sides of the equation:\n

1. **State the problem:** Solve for $b$ in the equation $$\frac{b}{2} + 1 = 3$$. 2. **Isolate the term with $b$:** Subtract 1 from both sides to get $$\frac{b}{2} = 3 - 1$$.

1. **Problem:** Factor the polynomial $$y^6 + 10y^5 - 24y^4$$ completely. 2. **Formula and rules:** To factor polynomials, first look for the greatest common factor (GCF). Then fac

1. **State the problem:** Solve the equation $2k=0$ for $k$. 2. **Formula and rules:** To solve for $k$, we want to isolate $k$ on one side of the equation. Since $k$ is multiplied

1. **Problem (a):** Calculate the dimensions of the smaller rectangle given that the area of the larger rectangle is 4 times the area of the smaller rectangle. 2. **Given:**

1. **State the problem:** Simplify the expression $|-11| + 4i^2 - 8(3 - 1)$. 2. **Recall important rules:**

1. **State the problem:** Simplify the expression $$\frac{(\frac{1}{2}b + 3a)^2 - (3a + \frac{1}{2}b)(3a - \frac{1}{2}b)}{3 - \frac{1}{3}a(3b + \frac{3}{5}a) + \frac{1}{5}a^2}$$. 2

1. We are asked to solve the equation $gf(x) = 1$ where \(f(x) = \frac{x+1}{2}\) and \(g(x) = \frac{2x+3}{x-1}\) with $x \in \mathbb{R}$ and $x \neq 1$. 2. First, find the expressi

1. **State the problem:** The sum of 3 and a number equals 4 times the number. We need to find the number. 2. **Set up the equation:** Let the number be $x$. The problem states:

1. The problem is to calculate $-16 \div \frac{8}{5}$.\n\n2. Division by a fraction is the same as multiplication by its reciprocal. So, we use the formula:\n$$a \div \frac{b}{c} =