🧮 algebra

1. **Stating the problem:** Solve the linear equation $8x + 9 = 4x + 12$ for $x$. 2. **Formula and rules:** To solve linear equations, we isolate the variable $x$ by performing the

1. **State the problem:** Simplify the expression $$\frac{8 - 5}{x - 12} = 51 = 5$$. 2. **Analyze the expression:** The expression as given is ambiguous because it shows $$\frac{8

1. The problem is to analyze the function $f(x) = x^2 - 2x + 1$. 2. This is a quadratic function in standard form. We can rewrite it to identify its properties.

1. The problem states: Start with 2 blue circles and 1 red square, then add 4 red squares each time. 2. We want to find the pattern rule for the number of red squares in each step.

1. The problem is to create a graph of a parabola similar to the one described, which opens upwards with a vertex near (1.5, 0). 2. The general form of a parabola is given by the q

1. **State the problem:** Solve the equation $$-22.5 = 3(3x - 4.5)$$. 2. **Use the distributive property:** Multiply 3 by each term inside the parentheses:

1. **State the problem:** Solve the equation $$10.5 = 4x - 4.5 - 3x$$ for $x$. 2. **Rewrite the equation:** Combine like terms on the right side.

1. **Stating the problem:** We are given vectors along a path and two diagonal vectors converging to a point, with a final vertical vector labeled 5. We want to analyze the vector

1. **Énoncé du problème :** Résoudre l'équation irrationnelle $$\sqrt{3x^2 + 2x + 4} = 2 - x$$. 2. **Formule et règles importantes :** Pour résoudre une équation avec une racine ca

1. **State the problem:** We are given the ratio of ages of Rahul and his sister as 4:3 currently, and 8 years ago, the ratio was 6:5. We need to find Rahul's current age. 2. **Set

1. The problem is to simplify the expression $-\left(\frac{-7}{-9}\right)$.\n\n2. Recall that a negative divided by a negative is positive, so $\frac{-7}{-9} = \frac{7}{9}$.\n\n3.

1. **State the problem:** Simplify the expression $-\left(-\frac{7}{9}\right) - \sqrt{\frac{49}{100}}$. 2. **Recall the rules:**

1. **Problemos uždavinys:** Arnas užrašė dviženklį skaičių, o Meinardas užrašė tą patį skaičių, bet sukeistais skaitmenimis. Meinardo skaičius yra 9 vienetais didesnis už Arno, o A

1. The problem asks if the function $y=\frac{1}{3}x^2 - 3$ is the same in standard form and vertex form. 2. The standard form of a quadratic function is generally written as $y = a

1. **State the problem:** Factor the expression $$y=\frac{3}{9}x^2 - 3$$. 2. **Simplify the coefficients:** $$\frac{3}{9} = \frac{1}{3}$$, so the expression becomes $$y=\frac{1}{3}

1. **State the problem:** Solve the equation $$\frac{n+6}{10} + \frac{2n}{20} = \frac{6}{3n}$$ for $n$. 2. **Identify the formula and rules:** To solve this equation, we need to fi

1. The problem is to solve the equation $y=2x-3$ in the $xy$-plane and find 4 points $(x,y)$ that satisfy this equation. 2. The equation $y=2x-3$ is a linear function where $y$ dep

1. **Stating the problem:** We need to find the system of inequalities that describes the shaded region in the given graph.

1. **State the problem:** Solve the inequality $$\frac{4x + 1}{5x - 3} \leq 2$$. 2. **Rewrite the inequality:** Subtract 2 from both sides to get a single rational expression:

1. The problem is to solve the equation $x - = $ for $x$. 2. Since the equation is incomplete, we assume it means $x - a = b$ where $a$ and $b$ are constants.

1. **State the problem:** Solve the equation $b \times b \times b = b + b + b$. 2. **Rewrite the equation:** The left side is $b^3$ (since $b \times b \times b = b^3$) and the righ