🧮 algebra

1. **State the problem:** Solve the equation $$-\frac{7}{3} - \frac{1}{4} u = \frac{1}{4}$$ for $u$. 2. **Isolate the term with $u$:** Add $$\frac{7}{3}$$ to both sides to move the

1. **State the problem:** We need to find the value of $a$ such that the slope of the line segment $CD$ is $2$, given points $C(-3, -2)$ and $D(1, a)$. 2. **Recall the slope formul

1. **Problem statement:** We are given four lines with equations:\n- $f(x) = -2x + 3$ (red line, downward slope)\n- $h(x) = x$ (green line, upward slope through origin)\n- $k(x) =

1. **State the problem:** We need to rewrite the circle equation $$x^2 + y^2 + 2x + 10y + 10 = 0$$ in standard form, find its center and radius. 2. **Recall the standard form of a

1. **State the problem:** We are given the circle equation $$x^2 + y^2 + 2x - 6y + 6 = 0$$ and need to write it in standard form, identify the center and radius, and select the cor

1. **State the problem:** We are given two equations: $a + b = 67$ and $a^b = 76$. We need to find the value of $b + d$. 2. **Analyze the problem:** We have two variables $a$ and $

1. The problem states: If $2^x = 18$, find $\log_2 18$. 2. Recall the definition of logarithm: If $a^x = b$, then $\log_a b = x$.

1. The problem states: If $2^x = 18$, then find the value of $2^{\log 18}$. 2. First, recall the definition of logarithm: $\log a$ means the logarithm base 10 of $a$.

1. **State the problem:** We are given two functions: $$f(x) = 3x^2 + 5x + 13$$

1. **State the problems:** - Problem 11 asks to plot all values where $X = -2$.

1. The problem asks to find the slope in the formula $Y = 4X + 5$. 2. The problem asks to find the Y-intercept in the formula $Y = -X + 3$.

1. **State the problem:** Determine whether the slope $m$ of each line is positive or negative based on the graph description and given values. 2. **Recall the rule for slope signs

1. The Y-intercept is the $y$-value when $x=0$. Given the point $(0, -3)$, the Y-intercept is $-3$. 2. A line with a negative slope slants \textbf{downward} to the right as $x$ inc

1. The problem asks to determine if the slope $m$ is positive or negative for each given value. 2. Recall the rule: If $m > 0$, the line rises from left to right (positive slope).

1. **State the problem:** Fill in the blanks for slope, intercept, and properties of parallel lines.

1. The problem asks to determine the value of $m$ for each given slope and whether it is positive or negative. 2. The slope $m$ is given as a fraction in each case, and the sign of

1. **State the problem:** Find the greatest common factor (GCF) of the polynomial expression $$3x + 5xy - 2x^5$$. 2. **Identify the terms:** The terms are $$3x$$, $$5xy$$, and $$-2

1. **State the problem:** We need to perform polynomial division for two expressions: a) $$\frac{-15y^2 - 11y + 2y^5 + 5}{2y - 1}$$

1. **State the problem:** Solve the equation $$8x - 2[3x + (4 - 2x)] = 2(5x + 1)$$ for $$x$$. 2. **Use the distributive property and simplify inside the brackets:**

1. **State the problem:** Solve the equation $$1 + \frac{1}{2} (7x - 10) + \frac{1}{2} x = 3x$$ for $x$. 2. **Use the distributive property:** Expand $$\frac{1}{2} (7x - 10)$$ to g

1. **State the problem:** Solve the equation $$\frac{1}{2}(-8x + 7) = -x - \frac{4}{3}(-9x + 3)$$ for $x$. 2. **Write the equation clearly:**