🧮 algebra

1. **Problem 1: Children and Adults in a Group** We have two variables: $x$ = number of children, $y$ = number of adults.

1. Let's understand why we write $2z$ and $2y$ in algebra. 2. When you see $2z$, it means $2 \times z$, which is the number 2 multiplied by the variable $z$.

1. **State the problem:** Add the numbers $5.5$ and $-2.5$. 2. **Recall the rule for adding positive and negative numbers:** When adding a positive number and a negative number, su

1. **Stating the problem:** We need to solve the system of inequalities:

1. **State the problem:** We need to add the numbers $5.1$ and $-6.1$. 2. **Recall the rule for adding positive and negative numbers:** When adding a positive number and a negative

1. Problem: Solve the system of equations for children ($x$) and adults ($y$): $$x + y = 2200$$

1. **State the problem:** Solve the equation $x - 740000 = x \times 25\%$ for $x$. 2. **Rewrite the percentage as a decimal:** $25\% = 0.25$.

1. The problem is to understand and work with the equation $x - y = z$. 2. This is a simple linear equation relating three variables $x$, $y$, and $z$.

1. Problema: Determinați valorile reale ale lui $x$ pentru care: $$\frac{1}{4x - 4} + \frac{1}{6x - 6} + \frac{1}{12x - 12} = \frac{1}{2x - 2}.$$

1. The problem is to solve a system of linear equations using the Gaussian elimination method. 2. Gaussian elimination involves transforming the system's augmented matrix into an u

1. **State the problem:** Solve the system of equations using the equal value method: $$3x + y = 8$$

1. **State the problem:** Solve the system of linear equations: $$3x + y = 8$$

1. Problema: Avem o progresie aritmetică cu termeni 2, 7, 12, 17, ... și trebuie să găsim rația acestei progresii. 2. Formula pentru rația unei progresii aritmetice este:

1. Problema ne cere să determinăm primii doi termeni ai unei progresii aritmetice în care următorii termeni sunt 10, 13, 16, ... 2. O progresie aritmetică este o succesiune de nume

1. **State the problem:** Solve the equation $$2 = \frac{100}{x}$$ for $x$. 2. **Formula and rules:** To solve for $x$ when it is in the denominator, multiply both sides of the equ

1. The problem involves understanding why the term $(-k+2)$ appears in step 4 of a previous solution. 2. Typically, $(-k+2)$ arises from rearranging or factoring expressions involv

1. Problem: Find the maximum value of the function $f(x) = -6x^2 + 3x - 4$. 2. This is a quadratic function in the form $f(x) = ax^2 + bx + c$ where $a = -6$, $b = 3$, and $c = -4$

1. **State the problem:** Solve for $y$ in terms of $r$ and $t$ in the proportion $$\frac{y - t}{3} = \frac{y - r}{5}.$$\n\n2. **Use cross-multiplication:** Multiply both sides by

1. El problema es resolver la ecuación dada (aunque no se especifica, asumiremos que se refiere a resolver una ecuación algebraica simple). 2. Para resolver una ecuación, usamos la

1. **State the problem:** We need to find the distance the bus travels between Hawkes Meadow and Brunswick Street. 2. **Identify the given information:**

1. **State the problem:** Solve the simultaneous equations for the variables involved. 2. **General approach:** To solve simultaneous equations, we use substitution or elimination