🧮 algebra

1. **State the problem:** Given the equation $$8x - \frac{2y}{3} = xy + y,$$ express $x$ in terms of $y$. 2. **Rewrite the equation:** Start by writing the equation clearly:

1. The problem asks to identify which inequality corresponds to the graph described. 2. The line crosses the y-axis at 5 and slopes downward, so the equation of the line is $y = -3

1. **State the problem:** Solve the equation $-3 = -4 + c$ for $c$. 2. **Isolate the variable:** To solve for $c$, add 4 to both sides of the equation to cancel out the $-4$ on the

1. **State the problem:** Solve the equation $-3 = -4 = c$ for $c$. 2. **Analyze the equation:** The equation $-3 = -4 = c$ is ambiguous because it suggests $-3 = -4$ and $-4 = c$

1. **State the problem:** Factorize the expression $54x^4 + 27x^3 a - 16x - 8a$. 2. **Group terms:** Group the expression into two parts to factor by grouping:

1. **State the problem:** Solve the quadratic equation formed by multiplying the binomials $\{5x-2\}$ and $\{2x-3\}$. This means we want to find $x$ such that $$(5x-2)(2x-3) = 0.$$

1. **State the problem:** Solve the quadratic equation $x^2 - 1x - 6 = 0$. 2. **Recall the quadratic formula:** For an equation $ax^2 + bx + c = 0$, the solutions are given by

1. **State the problem:** Solve the quadratic equation $$x(x-5)=0$$. 2. **Formula and rule:** The zero product property states that if $$ab=0$$, then either $$a=0$$ or $$b=0$$.

1. **Problem statement:** Calculate the value of $4.15$ multiplied by $50$ or $6$ using a scale factor. 2. **Formula:** To find the scaled value, use the multiplication formula:

1. **State the problem:** Solve the quadratic equation $x^2 - x = 0$. 2. **Formula and rules:** To solve quadratic equations, we can factorize the expression and use the zero produ

1. **State the problem:** Solve the quadratic equation $ (x-6)(x+3) = 0 $. 2. **Use the zero product property:** If the product of two factors is zero, then at least one of the fac

1. **State the problem:** Solve the equation $2(2x - 3) - (6x - 9) = 2x^2$ for $x$. 2. **Apply the distributive property:**

1. **State the problem:** Simplify the expression $\left(x-6\right)\left(x+3\right)$. 2. **Recall the distributive property (FOIL method):** When multiplying two binomials, multipl

1. **State the problem:** Solve for $x$ in the equation $3.8 = \frac{x}{7}$.\n\n2. **Formula and rule:** To solve for $x$ when it is divided by 7, multiply both sides of the equati

1. **State the problem:** Solve for $x$ in the equation $3.8 = \frac{x}{7}$.\n\n2. **Formula and rule:** To solve for $x$, multiply both sides of the equation by 7 to isolate $x$.\

1. ປະກາດບົດບັນຫາ: ຈົດແຕ່ລິມມີອຸ່ມນີ້ ກ. 3x^2 + 5x - 4 = 0 2. ໃຊ້ສູດສຳລັບສູດຄວາມສົມດຸນຄະນິຍາມສະກັດ (quadratic formula):

1. The problem is to understand what happens when the denominators in fractions are not the same. 2. When adding or subtracting fractions, the denominators must be the same to comb

1. **Problem statement:** Solve the first system of linear equations: $$\begin{cases} x + y = 3 \\ 2x + 3y = 7 \end{cases}$$

1. The problem is to simplify and find the value of the expression $$\frac{\sqrt{a \sqrt{a \sqrt{a}}}}{\sqrt[3]{a^{5/2} a}}$$. 2. First, rewrite the expression inside the radicals

1. The problem asks to compare two variables, $\alpha$ and $\beta$, in different situations. 2. To compare $\alpha$ and $\beta$, we need to understand the context or the mathematic

1. **Problem 1: Addition of Integers** The temperature starts at $-7^\circ C$ and changes by $+5^\circ C$, $-3^\circ C$, and $+8^\circ C$ over three hours.