🧮 algebra

1. Solve $10x - 4 = 7x - 16$. Move terms with $x$ to one side: $10x - 7x = -16 + 4$

1. **Statement of the problem:** We are given the equation $$\sqrt{k - x} = 58 - x$$ where $$k$$ is a constant. The equation has exactly one real solution. We need to find the mini

1. **State the problem:** Simplify the expression $\left(6^{-4} \cdot 8^{-7}\right)^{-9}$. 2. **Apply the power of a product rule:** When raising a product to a power, raise each f

1. **State the problem:** Simplify the expression $$\frac{4^{11}}{4^{-8}}$$ and rewrite it in the form $$4^n$$. 2. **Recall the rule for dividing powers with the same base:** When

1. The problem asks us to simplify the expression $$z^{-11} \cdot z^{-15}$$ and rewrite it in the form $$z^n$$. 2. Recall the rule for multiplying powers with the same base: $$a^m

1. **State the problem:** Simplify the expression $$a^{-13} \div a^{-6}$$ and rewrite it in the form $$a^n$$. 2. **Recall the rule for dividing powers with the same base:** When di

1. The problem is to simplify the expression: $\sqrt{7} \cdot 2\sqrt{3} - \sqrt{6}$.\n\n2. First, multiply $\sqrt{7}$ and $2\sqrt{3}$: \n$$\sqrt{7} \cdot 2\sqrt{3} = 2 \cdot \sqrt{

1. **Stating the problem:** We want to understand the general concept of functions, especially for beginners in 1st year Baccalaureate (1bac) in Morocco, explained in English with

1. **Déterminer la fonction du revenu et sa forme** Le propriétaire attire 200 spectateurs à un prix de 3,50 et 70 spectateurs de plus si le prix baisse. On suppose une relation li

1. **Solve the first equation:** $2x - 2x + 9 = 6x - 2x - 7$ Simplify both sides:

1. Solve $10x - 4 = 7x - 16$: Subtract $7x$ from both sides: $10x - 7x - 4 = -16$

1. The problem involves simplifying expressions with square roots and fractions. 2. First, simplify the expression $2\sqrt{5} + 5\sqrt{5}$ over 10:

1. Given the problem: If $\beta(m,n) = 6$ and $\Gamma(m,n) = 120$, find $\Gamma_m \Gamma_n$. 2. We need to understand the relationship between $\beta(m,n)$, $\Gamma(m,n)$, and $\Ga

1. **State the problem:** We know that $h$ is inversely proportional to $v$, which means $h = \frac{k}{v}$ for some constant $k$. 2. **Find the constant $k$:** Given $h = 8$ when $

1. The problem states that $y$ is inversely proportional to $x$, which means $y \propto \frac{1}{x}$. This can be written as an equation with a constant $k$: $$y = \frac{k}{x}$$ 2.

1. The problem states that $t$ is proportional to $w^2$, which means we can write the equation as: $$t = k w^2$$

1. **State the problem:** We are given the equation $y = kx^2$ and the values $y = 128$ when $x = 4$. We need to find the value of $k$. 2. **Substitute the known values:** Substitu

1. The problem is to analyze the inequality $$-54r + 40c - 50w - 94n + 74a - 36 < 489$$ and identify its components. 2. A **coefficient** is the numerical factor multiplying a vari

1. The problem is to identify the parts of the expression and equation: $-18u + -85i + -33 = -114$. 2. **Coefficient**: The numerical factor multiplying a variable. Here, coefficie

1. **State the problem:** We know the height of a tree and the length of its shadow are directly proportional. 2. **Given data:**

1. The problem is to identify parts of the inequality $35c + -81v + -68 > 199$. 2. A **coefficient** is a number multiplying a variable. Here, $35$ is the coefficient of $c$, and $