🧮 algebra

1. The first equation is given as $3. (3x - 1) + 1) (1 - 3x) = 0$. Likely, the intended expression is $(3x - 1 + 1)(1 - 3x) = 0$. Simplify inside the parentheses: $3x - 1 + 1 = 3x$

1. Stating the problem: Solve the quadratic equation $x^2 - 3x + 2 = 0$ using factorization. 2. To factorize, look for two numbers that multiply to the constant term $2$ and add up

1. The problem is to solve the system of linear equations $$\begin{cases} a_1 x + b_1 y = c_1 \\ a_2 x + b_2 y = c_2 \end{cases}$$

1. The problem is to solve the quadratic equation $$x^2 - 5x + 6 = 0.$$\n\n2. To solve this quadratic equation, we can factor it. We look for two numbers that multiply to $6$ and a

1. Stating the problem: We want to solve the inequality $$5^{\frac{x^2 - 3x}{2x - 4}} \leq 5.$$\n\n2. Since the base 5 is positive and greater than 1, the exponential function is i

1. The problem is to solve the equation $$\left| \frac{9 - x^2}{x - 1} \right| = \frac{x^2 - 9}{x - 1}$$. 2. Notice that $$x^2 - 9 = (x - 3)(x + 3)$$ and $$9 - x^2 = -(x^2 - 9) = -

1. সমস্যাটি হলো, আমরা অনুসন্ধান করবো কতগুলি পাথর বার করা হয়েছে, যেখানে নিচের শর্তগুলি দেওয়া আছে: ৮ ফল সামনে, ১ ০ ফল পূর্ণ হলে পাথর পারলে ৬ ফল আর \(x\) ফল বাদলে \(x+6\) ফল হবে। 2.

1. Vous mentionnez que c'est la même équation que la précédente. 2. Sans plus de détails, je ne peux pas résoudre ou analyser l'équation.

1. **State the problem:** Solve the inequality $$\frac{x^2 - 3x}{2x - 4} \leq 5$$. 2. **Rewrite the inequality:** Bring all terms to one side to get a single rational expression.

1. **State the problem:** We are given the equation $\log_x y + 6 \log_x (2^3) = 3$ and need to express $y$ in terms of $x$. 2. **Rewrite powers inside the logarithm:** Note that $

1. Problem: Calculate the sum $$\frac{6}{7} + \frac{1}{10} + \frac{8}{9}$$. 2. Find a common denominator for 7, 10, and 9. The least common multiple is $630$.

1. **State the problem:** Given that \(\log_x y + 6 (\log_x 2)^3 = 3\), express \(y\) in terms of \(x\).

1. **State the problem:** Given the equation $\log_x y + 6 \log_x (2^3) = 3$, express $y$ in terms of $x$. 2. **Rewrite the logarithmic terms:** Note that $2^3 = 8$, so $6 \log_x (

1. The problem given is to solve the equation $\log_x y + 6 \log_x 2^3 = 3$. 2. First, simplify the expression inside the logarithm: since $2^3 = 8$, the equation becomes $\log_x y

1. State the problem: Solve and simplify the equation $$16x^2+4y^2+32x-16y-32=0$$. 2. Group terms by variables: $16x^2+32x + 4y^2 -16y = 32$

1. We are given the equation of a conic: $$16x^2 + 25y^2 + 160x + 200y + 400 = 0$$. 2. First, group the $x$ and $y$ terms:

1. **State the problem:** We are asked to graph the inequality $-3x + 2y > 6$ and determine where the shaded region is. 2. **Rewrite the inequality:** To graph the inequality, firs

1. **State the problem:** We need to graph the inequality $3x - y \leq 4$ and find three points that satisfy this condition. 2. **Rewrite the inequality:** Rearrange to a more fami

1. Problem: Graph the inequality $$3x - y \leq 4$$ and show the shaded region. 2. Rewrite the inequality to express $$y$$ in terms of $$x$$:

1. The problem is to graph the inequality $3x - y \leq 4$. 2. First, rewrite the inequality to express $y$ in terms of $x$:

1. **Problem Statement:** Find the ratio in which the point $(a,3)$ divides the line segment joining the points $(11,-2)$ and $(3,6)$, and calculate the value of $a$. 2. **Step 1: