🧮 algebra

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:

1. Let's start by identifying the formula you provided in your first task. 2. Once we have the formula, we can break it down into its components and understand its structure.

1. The problem: Solve $2x+3=7$ for $x$. 2. Subtract $3$ from both sides: $2x=7-3$

1. **State the problem:** Simplify the expression $$\frac{5^{x - y} \times 125^{3x - y}}{25^x}$$. 2. **Rewrite bases with the same base if possible:** Note that 125 and 25 can be e

1. **State the problem:** Solve the given exponential and logarithmic expressions and simplify the fraction involving powers of 5 and 25. 2. Evaluate the expression $x \log 6 = 7 \

1. The problem is to solve the equation $X^2 - 8X - 5 = (X - 4)^2 - 11$ for $X$. 2. First, expand the right side: $(X - 4)^2 = X^2 - 8X + 16$.

1. Stating the problem: Solve the equation $9x - 10 = 5x + 2(2x - 5)$ for $x$. 2. Expand the right side: $2(2x - 5) = 4x - 10$.

1. State the problem: Solve the equation $9x - 10 = 5x + 2(2x - 5)$. 2. Distribute the 2 on the right side: $9x - 10 = 5x + 4x - 10$.