🧮 algebra

1. **State the problem:** Solve the compound inequality $$-5 < \frac{x - 4}{2} \leq 1$$ and express the solution in the form $$a < x \leq b$$. 2. **Isolate the variable:** Multiply

1. **State the problem:** Solve the compound inequality $$16y - 18 > 46 \text{ OR } 14y + 6 < 20.$$ 2. **Solve the first inequality:** $$16y - 18 > 46.$$

1. **State the problem:** Solve the compound inequality \(3m + 2 < 5\) or \(\frac{m + 1}{2} > 4\). 2. **Solve the first inequality:**

1. **Problemstellung:** Wir haben drei Taxiunternehmen mit unterschiedlichen Preisstrukturen und sollen die Fahrpreise als Terme angeben, Werte berechnen, Schaubilder zeichnen, ver

1. The problem asks to determine the interval where the parabola is decreasing. 2. The parabola opens upwards and has its vertex at approximately $(3, -7)$.

1. **State the problem:** Calculate the value of $5^3 \times 6^6$. 2. **Calculate each power separately:**

1. The problem is to analyze the function $f(x) = e^{[x]}$ where $[x]$ is the greatest integer function (floor function) and $x \in [-4, 2]$. 2. The greatest integer function $[x]$

1. The problem is to analyze the function $f(x) = e^x$ for $x \in [-4, 2]$. 2. The function $f(x) = e^x$ is an exponential function where the base $e$ is approximately 2.718.

1. **Stating the problem:** Lisa’s Quick Stop sells milk at a price 2% below the main grocery store. We are given Lisa’s prices for 8 weeks and want to find the corresponding main

1. The problem is to solve the equation fully. Since no specific equation is given, let's consider a general approach to solving algebraic equations. 2. Identify the type of equati

1. **State the problem:** Solve for the roots of the equation $$x^4 + 5x = 7$$ in closed form. 2. **Rewrite the equation:** Move all terms to one side to set the equation to zero:

1. **State the problem:** Calculate the value of $2^{10} \times 5^{10} \times 10^{15}$. 2. **Rewrite the expression:** Notice that $10 = 2 \times 5$, so $10^{15} = (2 \times 5)^{15

1. The problem is to graph the line and write the function for $y = 3x + 2$. 2. This is a linear function where the slope is 3 and the y-intercept is 2.

1. The problem is to understand the average growth factor over 6 years using the geometric mean, which Bob calculated as 1.24. 2. The geometric mean $G$ of $n$ growth factors $g_1,

1. Masalah: Gambarkan garis dan fungsi dari persamaan $y = 3x + 2$. 2. Fungsi yang diberikan adalah fungsi linear dengan bentuk umum $y = mx + c$, di mana $m = 3$ adalah gradien da

1. Masalah yang diberikan adalah menggambarkan garis dari fungsi linear $y = 3x + 2$. 2. Fungsi ini adalah fungsi linear dengan gradien (kemiringan) $3$ dan intercept $y$ pada $2$.

1. The problem involves evaluating and simplifying expressions with exponents (potencias). 2. Let's clarify and solve the expressions step-by-step:

1. The problem is to solve the quadratic equation $x^2 + 2x - 8 = 0$. 2. We start by trying to factor the quadratic expression. We look for two numbers that multiply to $-8$ and ad

1. **State the problem:** Solve the quadratic equation $$x^2 + 2x - 8 = 0$$ and analyze its graph. 2. **Identify coefficients:** Here, $$a = 1$$, $$b = 2$$, and $$c = -8$$.

1. **Problem Statement:** Draw a rough sketch of the graph of a line where the slope $m < 0$ and the y-intercept $c > 0$.

1. The problem asks to calculate the gradient (slope) of the straight line passing through the points $(-3, -2)$ and $(1, 6)$.\n\n2. The formula for the gradient $m$ between two po