🧮 algebra

1. **State the problem:** Simplify the expression $$\frac{2a - 3b5'}{(2a - 1b)3}$$. 2. **Interpret the expression:** The numerator is $$2a - 3b5'$$ and the denominator is $$(2a - 1

1. **Stating the problem:** A quadratic equation is any equation that can be written in the form $$ax^2 + bx + c = 0$$ where $a$, $b$, and $c$ are constants and $a \neq 0$. 2. **Me

1. **State the problem:** The heights of two poles are in the ratio 9:5. The height of the shorter pole is 8 m. Find the height of the taller pole. 2. **Formula and rules:** If two

1. The problem asks to write inequality statements as mathematical expressions. 2. Inequality statements compare two values using symbols: greater than ($>$), less than ($<$), grea

1. **Problem 2:** The heights of 2 poles are in a ratio of 9:5. The height of the shorter pole is 8 m. What is the height of the taller pole? 2. **Set up the proportion:** Let the

1. **State the problem:** We need to find how many students at Pierrefonds Comprehensive High School are learning to play the guitar. 2. **Given information:**

1. **State the problem:** Multiply the fractions $\frac{7}{8}$ and $\frac{6}{1}$. 2. **Formula used:** To multiply fractions, multiply the numerators together and the denominators

1. **State the problem:** Solve the equation $x - y = 11$ for one variable in terms of the other. 2. **Formula and rules:** This is a linear equation in two variables. To express o

1. **State the problem:** Solve the equation $x - y = 11$ for one variable in terms of the other. 2. **Formula and rules:** This is a linear equation in two variables. To express o

1. **State the problem:** Simplify the expression $-(5f+2)+5f$. 2. **Apply the distributive property:** The negative sign before the parentheses means we multiply each term inside

1. **State the problem:** Simplify the expression $$\frac{2}{x-3} + \frac{3}{x+2} - \frac{4x-7}{x^2 - x - 6}$$. 2. **Identify the denominator factorization:** The quadratic in the

1. **State the problem:** Simplify the expression $$\frac{2}{x-3} + \frac{3}{x+2}$$. 2. **Formula and rules:** To add rational expressions, find a common denominator, which is the

1. **State the problem:** Simplify the expression $$\frac{4a^2-(x-3)^2}{(2a+x)^2-9}$$. 2. **Recall formulas:** This expression involves differences of squares. Recall that $$A^2 -

1. **State the problem:** Simplify the expression $$(2a + x)^2 - 9$$. 2. **Recall the formula:** The square of a binomial is given by $$(A + B)^2 = A^2 + 2AB + B^2$$.

1. **State the problem:** Multiply out the brackets and simplify the expression $3(3n-2)+5$. 2. **Recall the distributive property:** To multiply a number by a bracket, multiply th

1. **State the problem:** Solve the equation $9 = 3 + \frac{x}{4}$ for $x$. 2. **Isolate the variable term:** Subtract 3 from both sides to get

1. **Stating the problem:** We have a sequence $(u_n)$ with terms $U_0, U_1, U_2, U_3, U_4$, and we want to understand the sum $12 (U_0 + U_1 + U_2 + U_3 + U_4)$ which represents t

1. Das Problem lautet: Finde die Nullstellen der Funktion $$f(x) = -2x^3 + 12x^2 - 18x$$. 2. Um die Nullstellen zu finden, setzen wir $$f(x) = 0$$ und lösen die Gleichung:

1. **State the problem:** Solve the linear equation $3x + 5 = 11$ for $x$. 2. **Formula and rules:** To solve for $x$, isolate $x$ on one side of the equation by performing inverse

1. Das Problem lautet: Finde die Nullstellen der Funktion $f(x) = x^3 - 6x$. 2. Nullstellen sind die Werte von $x$, für die $f(x) = 0$ gilt.

1. **State the problem:** Solve the equation $$\left(4y\right)^{\frac{1}{3}} + 3 = 5$$ for $y$. 2. **Isolate the cube root term:** Subtract 3 from both sides: