🧮 algebra

1. **Problem Statement:** Sketch the graph of the function $$y = \sqrt{-2(x - 4)} - 5$$ and understand its transformations.

1. The problem asks to write the expression $-9x^{-1}$ without negative exponents and without parentheses. 2. Recall the rule for negative exponents: $a^{-n} = \frac{1}{a^n}$ where

1. **State the problem:** We need to solve the given algebraic problem step-by-step, showing all intermediate work and explanations. 2. **Identify the formula or approach:** Since

1. **State the problem:** Find the slope of the line passing through the points $(-3, 2)$ and $(4, -5)$.\n\n2. **Formula for slope:** The slope $m$ of a line through points $(x_1,

1. **State the problem:** We need to find the slope of the line passing through the points $(-3, -2)$ and $(2, 4)$. 2. **Recall the formula for slope:** The slope $m$ of a line thr

1. **Stating the problem:** Simplify the expression $$(3x + 7) - (-2x - 5) + (8x + 2) - (-x + 6)$$. 2. **Recall the rule:** When subtracting a quantity in parentheses, change the s

1. Stating the problem: Simplify the expression $X2 - 2x2$. 2. Understanding the expression: It looks like the expression involves variables and numbers. Assuming $X2$ means $X \ti

1. **State the problem:** Solve the equation $$2(3x + 2) = 2x + 28$$ for $x$. 2. **Apply the distributive property:**

1. **State the problem:** We are given that the price of a plain bowl of phở is $b$ and the price of each extra ingredient is $n$. The total price of a plain bowl plus 3 extra ingr

1. **State the problem:** We have a bar model representing the total price of a bowl of plain phở plus some extra ingredients. The bar is divided into 4 segments: one segment label

1. **Problem:** Simplify the rational expression $$\frac{3(x + 2)}{9(x + 3)}$$ given $$x \neq -3$$. 2. **Formula and rules:** To simplify a rational expression, factor numerator an

1. **State the problem:** We are given the expression $96x^3 - 12x^2 - 112x + 14$ and a sequence of factorizations:

1. **State the problem:** Simplify the expression $$\frac{6x - 1}{3x - 4} + \frac{4x - 1}{4 - 3x}$$ given the restrictions $$x \neq 4$$ and $$x \neq -1$$. 2. **Identify the restric

1. **State the problem:** Solve the system of equations by graphing: $$2x + y = 2$$

1. **State the problem:** Solve the equation $7A = -2[-7 - 3(4) + 5 - 2(-1)] + 3(6 + 8)$. 2. **Apply the order of operations:** Start by simplifying inside the brackets and parenth

1. Stating the problem: Simplify the expression $$3 \left(\frac{11}{12} - \frac{5}{6}\right) + \frac{3}{4}$$. 2. Use the order of operations: first simplify inside the parentheses,

1. The problem asks to find the constant of proportionality for each proportional relationship given in the table and for the equation $y=1.3x$. 2. The constant of proportionality

1. **State the problem:** Simplify the expression $-5(6m + 3) - 7(-7m + 7)$. 2. **Apply the distributive property:** Multiply each term inside the parentheses by the factor outside

1. **State the problem:** Simplify the expression $-4(8f + g) + 9g - 5(-2g + 6f)$. 2. **Apply the distributive property:** Multiply each term inside the parentheses by the factor o

1. **Stating the problem:** We need to find the value of $x$ in an addition problem where the total was mistakenly taken as 540 instead of 431. 2. **Understanding the problem:** If

1. The problem involves evaluating the function $g(x)$ at specific points and understanding the range of $g$. 2. Part A states the range is $(-\infty, 4]$. This means $g(x)$ can ta