🧮 algebra

1. **State the problem:** Simplify the expression $-5 - 5 + 6$. 2. **Apply the rules of addition and subtraction:** When adding and subtracting integers, combine the numbers step-b

1. The problem is to evaluate the expression $6 - 5 \times 3 - 2$. 2. According to the order of operations (PEMDAS/BODMAS), multiplication must be done before addition and subtract

1. **State the problem:** Simplify the expression $$\frac{8}{9} - \frac{4}{5} + \frac{1}{6}$$. 2. **Find a common denominator:** The denominators are 9, 5, and 6. The least common

1. **State the problem:** Simplify the expression $$\frac{7}{8} - \frac{1}{4} - \frac{2}{5}$$. 2. **Find a common denominator:** The denominators are 8, 4, and 5. The least common

1. **Problema:** Resolver la expresión $$\frac{1}{2} - \left[\frac{3}{4} \times 5 + 2 \times \left(-\frac{3}{4} \times 2 + 5\right)\right] + \frac{5}{2}$$. 2. **Fórmulas y reglas:*

1. **Problema:** resolver los siguientes cálculos en $\mathbb{R}$. **a)** $$\frac{1}{2}-4+\left(\frac{3}{5}+\frac{1}{2}\right)^2$$

1. **State the problem:** Solve the quadratic equation $X \times x + 9 = 0$. 2. **Rewrite the equation:** The equation can be written as $Xx + 9 = 0$.

1. **Problem 1: Evaluate $\frac{3ac}{b}$ given $a=4$, $b=-2$, and $c=-3$.** 2. Use the formula:

1. **Problem:** Given that $a = 4$, $b = -2$, and $c = -3$, evaluate $\frac{3ac}{b}$. 2. **Formula:** The expression is $\frac{3ac}{b}$. We substitute the values of $a$, $b$, and $

1. El problema nos pide hallar dos cosas: (a) el valor de $f(-4)$ y (b) un valor de $x$ tal que $f(x) = -5$. 2. Observando el gráfico, la función $f$ es una parábola con vértice ap

1. The problem asks for the slope of a line perpendicular to the line given by the equation $$y = 4x + \frac{3}{2}$$. 2. Recall that the slope-intercept form of a line is $$y = mx

1. **State the problem:** David can plant 300 flowers in the same time Sarah plants 240 flowers. David plants 10 more flowers per hour than Sarah. We want to find Sarah's planting

1. Let's create a similar algebra problem for practice. 2. Problem: Solve for $x$ in the equation $$3x - 7 = 2x + 5$$.

1. **State the problem:** We have two customers buying cheese and milk. The first customer pays 12.45 dollars for 1 pound of cheese and 2 gallons of milk. The second customer pays

1. **State the problem:** Solve the inequality $$\frac{3}{4}(x + 8) > \frac{1}{2}(2x + 10)$$ and graph the solution on a number line. 2. **Write the inequality:** $$\frac{3}{4}(x +

1. **State the problem:** We need to determine which values of $x$ satisfy the inequality $$4(2 - x) > -2x - 3(4x + 1).$$ 2. **Expand both sides:**

1. **State the problem:** Simplify the expression $$(-2)^2 - (-2)(+3) + (-2)^7 : (-2)^4 - [(-2)^8 \times (-2)^2] : (-2)$$ where ":" denotes division. 2. **Recall the rules:**

1. **Problem:** Factorise the quadratic expression $x^2 + 7x + 12$. 2. **Formula and rules:** To factorise a quadratic expression of the form $x^2 + bx + c$, find two numbers that

1. **State the problem:** Simplify the expression $$- \frac{1}{16} : (x+2)(x+2)(x-3)(x-3)$$ which means dividing $$- \frac{1}{16}$$ by the product $$(x+2)^2 (x-3)^2$$. 2. **Rewrite

1. **Problem:** Find $x$ such that $$(x-1)^3 = 4^3$$ 2. **Formula and rules:** For equations of the form $a^3 = b^3$, if $a$ and $b$ are real numbers, then $a = b$.

1. Planteamos el problema: Analizar la función por partes $$F(x) = \begin{cases} x^2 - x, & x \leq 1 \\ x^3 - 8, & 1 < x \leq 2 \end{cases}$$ y graficarla. 2. Para cada rama, ident