🧮 algebra

1. The problem is to solve the equation $2x + 3 = 11$ for $x$. 2. The formula used here is to isolate $x$ by performing inverse operations. We subtract 3 from both sides and then d

1. **State the problem:** Solve the inequality and equation system: $$3(2+x) \leq 4x = 1$$. 2. **Analyze the problem:** The expression seems to combine an inequality and an equatio

1. The problem is to solve the equation given by the user. However, no specific equation was provided, so I will demonstrate solving a simple algebraic equation as an example: Solv

1. Let's solve the first problem: Verify if the ratio $1.5 : 350$ equals $1 : 70$. 2. The ratio $a : b$ equals $c : d$ if and only if $\frac{a}{b} = \frac{c}{d}$.

1. **State the problem:** Manny's Pizza has monthly net profits following an arithmetic sequence: 4, 1, -2, -5, ..., -56 (in hundreds of dollars). We need to find the total profit

1. **State the problem:** Solve the equation $$\frac{1}{2}|x + 1| + 1 = |x|$$ using the graph. 2. **Understand the functions:** The left side is $$y = \frac{1}{2}|x + 1| + 1$$, a V

1. **Problem Statement:** Determine if the function $f(x) = \frac{x+4}{x-2}$ is continuous at $x = -2$ and $x = 0$. 2. **Recall the definition of continuity at a point $c$: **

1. **State the problem:** We have three groups of workers: skilled, semi-skilled, and unskilled. Total workers = 45. 2. **Define variables:** Let $x$ = number of skilled workers, $

1. **State the problem:** Simplify the expression $$\sqrt[4]{16 a^4 b^{16}}$$ where $a$ and $b$ are real numbers. 2. **Recall the formula:** The fourth root of a product is the pro

1. The problem is to simplify the expression $-\sqrt{36x^2}$ assuming $x$ is a positive real number. 2. Recall the property of square roots: $\sqrt{a^2} = |a|$. Since $x$ is positi

1. نبدأ بكتابة المعطيات: أ = 2 ب 2. المطلوب إثباته هو: $$\frac{n + 5 ب}{7 - أ} < ب$$

1. نبدأ بكتابة المعطيات: أ = ب أتين ٨ أ ه ب 2. نلاحظ أن المعطى غير واضح تمامًا، ولكن سنفترض أن المطلوب هو حل المعادلة أو تبسيطها.

1. نبدأ بكتابة المعطى: $$\frac{م - ه}{ن - ب} = \frac{ن + ه}{ب - م}$$

1. **State the problem:** Solve for $r$ in the equation $x = \frac{r+1}{r}$. 2. **Rewrite the equation:** Multiply both sides by $r$ to eliminate the denominator:

1. **State the problem:** Solve the system of equations using the substitution method: $$2m + n = 0$$

1. **Problem:** A car travels 780 kilometers in 12 hours. Find the speed of the car. 2. **Formula:** Speed is calculated by dividing distance by time:

1. **State the problem:** We start with the quadratic function $$f(x) = x^2 - 3x + 4$$ and apply three transformations in order: reflection in the x-axis, horizontal shift 2 units

1. **State the problem:** Solve the equation $$|3x - 45| = 12x$$ and check the solutions. 2. **Recall the definition of absolute value:** For any expression $A$, $$|A| = \begin{cas

1. **State the problem:** Given the input-output pairs of a function: input $3,6,8,n$ and output $6,12,16,\square$, find the output when the input is $n$. 2. **Analyze the pattern:

1. The problem involves understanding the vertical line along the y-axis from -5 to -10. 2. A vertical line along the y-axis means the x-coordinate is constant, specifically $x=0$.

1. The problem asks to determine the coordinates of the vertex of a parabola from its graph. 2. The vertex of a parabola given by the equation $y = ax^2 + bx + c$ is the point wher