🧮 algebra

1. **State the problem:** Use the distributive property to expand the expression $3(b + 9)$. 2. **Recall the distributive property formula:** For any numbers $a$, $b$, and $c$,

1. **State the problem:** Evaluate the expression $$-\frac{1}{8} - \left(-\frac{1}{5}\right)$$. 2. **Understand the operation:** Subtracting a negative is the same as adding a posi

1. The problem is to evaluate the expression $\frac{3}{8} - \left(-\frac{1}{12}\right)$.\n\n2. When subtracting a negative number, it is equivalent to adding the positive of that n

1. The problem is to solve question 12 (details not provided, so assuming a typical algebraic problem). 2. Since the exact problem is not given, let's assume question 12 involves s

1. The problem is to simplify or understand the expression involving $r/12$ instead of $\pi/12$. 2. We start by clarifying the difference: $r/12$ means the variable $r$ divided by

1. **State the problem:** Solve the equation $$\frac{\pi}{12} - 11 = -5$$ for the unknown or verify the equality. 2. **Understand the equation:** The equation involves a constant t

1. The problem is to solve the equation given by the user, but since no specific equation was provided, I will demonstrate solving a simple algebraic equation as an example: Solve

1. **State the problem:** We need to find the slope $m$ of the line given by the equation $y = \frac{3}{2}x$. 2. **Recall the slope formula:** The slope-intercept form of a line is

1. **State the problem:** Simplify the complex fraction $$\frac{7 - 17i}{2 - 3i}$$ into the form $a + bi$ where $a$ and $b$ are real numbers. 2. **Formula and rule:** To simplify a

1. The problem asks to write ratios comparing cups of cereal to cups of pecans, identify the type of ratio, find the total snack mix amount, write ratios comparing each ingredient

1. The problem is to simplify the expression given by the user. 2. Since no specific expression was provided, simplification generally involves combining like terms, factoring, or

1. The problem involves writing and understanding ratios between quantities such as cups of cereal and cups of pecans, balloons blown up by Leo and Kathy, and tickets sold by class

1. **State the problem:** Solve the equation $$15 \cdot 8(3b + 1) = 4(7b + 3) - 9$$ for $b$. 2. **Rewrite the equation:** The problem is to find $b$ such that $$15 \times 8(3b + 1)

1. **State the problem:** Put the equation $3x - y = -6$ into slope-intercept form. 2. **Recall the slope-intercept form:** The slope-intercept form of a line is given by $$y = mx

1. **State the problem:** Put the equation $3x - 6y = -30$ into slope-intercept form, which is $y = mx + b$ where $m$ is the slope and $b$ is the y-intercept. 2. **Isolate $y$:** S

1. **State the problem:** Put the equation $12y - 9x = -36$ into slope-intercept form $y = mx + b$. 2. **Recall the slope-intercept form:** The slope-intercept form of a line is $$

1. **State the problem:** Solve for $x$ in the equation $$-3(2x - 6) = -5 - (x - 8)$$. 2. **Apply the distributive property:** Multiply $-3$ by each term inside the parentheses on

1. **State the problem:** Solve for $x$ in the equation $$-4x + 2(x + 4) = -7x - (x + 1)$$. 2. **Apply the distributive property:** Expand the terms with parentheses.

1. **State the problem:** Solve for $x$ in the equation $$7x - 3(9x + 4) = 9(-x - 1) + x.$$\n\n2. **Apply the distributive property:** Multiply inside the parentheses:\n$$7x - 3 \t

1. **State the problem:** Solve for $x$ in the equation $$-x - (-7x - 4) = 8x + 6(-x + 5).$$ 2. **Apply the distributive property and remove parentheses:**

1. The problem involves understanding and comparing ratios in different forms: part-to-part, part-to-whole, and whole-to-part. 2. Ratios compare quantities and can be written as fr