🧮 algebra

1. **Problem:** Calculate $$\left(-\frac{8}{15}\right) \times \left(7 \frac{1}{4} - 3 \frac{1}{2}\right)$$. 2. **Convert mixed numbers to improper fractions:**

1. **State the problem:** Simplify the expression $$(3 + 6n^5 - 8n^4) - (-6n^4 - 3n + 8n^5).$$ 2. **Recall the rule:** When subtracting a polynomial, distribute the minus sign to e

1. **State the problem:** Simplify the expression $$(4n - 3n^3) - (3n^3 + 4n)$$. 2. **Apply the distributive property:** Remove the parentheses by distributing the minus sign to th

1. **State the problem:** Simplify the expression $$(4r^3 + 3r^4) - (r^4 - 5r^3).$$ 2. **Apply the distributive property:** Remove the parentheses by distributing the minus sign to

1. The problem is to simplify the expression $$(3a^2 + 1) - (4 + 2a^2)$$. 2. Use the distributive property to remove the parentheses: $$3a^2 + 1 - 4 - 2a^2$$.

1. **State the problem:** We want to find the population of Bigtimeville in the year 2008 given that in 2025 the population is 63,881 and the net growth rate is $\frac{8}{1000}$ pe

1. The problem asks to evaluate $|(-16) + (-4)|^2$. 2. First, simplify inside the absolute value: $(-16) + (-4) = -20$.

1. The problem asks to evaluate $\left(\frac{36}{6}\right)^3$. 2. First, simplify the fraction inside the parentheses: $\frac{36}{6} = 6$.

1. **State the problem:** Simplify and solve the equation $$\frac{3x - 1}{6x - 3} + \frac{1}{4x^2 - 1} = \frac{-x}{2x + 1}.$$\n\n2. **Identify and factor denominators:**\n- $6x - 3

1. **State the problem:** Simplify the expression $$2 - \frac{3x+2}{x+2} - \frac{2}{7}(2-x)$$. 2. **Rewrite the expression:**

1. **State the problem:** Solve the equation $$(4x+1)(x+3)-3(x-2)=(2x-3)^2$$ for $x$. 2. **Expand both sides:**

1. **State the problem:** Find the inverse of the function $$f(x) = (x - 3)^2 + 3$$ for $$x \geq 3$$ and verify the result. 2. **Recall the definition of inverse function:** The in

1. **State the problem:** Find the explicit form of the function $y$ from the equation

1. Énoncé du problème : La largeur d'un rectangle est 1 cm de plus que la moitié de sa longueur. Le périmètre est de 86 m. Trouvons les dimensions du rectangle. 2. Formule du périm

1. **State the problem:** Solve the inequality $8 < 2 - 2(3x - 1) + \frac{4}{5}x$. 2. **Apply distributive property:** Expand $-2(3x - 1)$ to get $-6x + 2$.

1. **State the problem:** Solve the inequality $-x - \frac{5}{2} \geq -8 + \frac{1}{2}(-x + 1)$.\n\n2. **Write down the inequality:** $$-x - \frac{5}{2} \geq -8 + \frac{1}{2}(-x +

1. Stwierdzenie problemu: Rozwiążmy równanie tożsamościowe $$4mn \times x = mn + x + \frac{1}{2}$$ dla zmiennej $x$. 2. Przepiszmy równanie: $$4mnx = mn + x + \frac{1}{2}$$

1. **Planteamiento del problema:** Resolver la ecuación $2(x+1)-3(x-2)=5(x+4)$. 2. **Expansión y simplificación:** Aplicamos la distributiva:

1. **Problem:** Solve the quadratic equation $3x^2 - 5x - 9 = 0$ using the quadratic formula and give answers correct to 2 decimal places. 2. **Formula:** The quadratic formula is

1. **Problem:** Solve the quadratic equation $3x^2 - 5x - 9 = 0$ using the quadratic formula and give answers correct to 2 decimal places. 2. **Formula:** The quadratic formula is

1. The problem is to draw the graphs of the two linear equations: $$x - 5y = 6$$