🧮 algebra

1. **Problem Statement:** Solve part (a) and (b) of question 8.

1. **State the problem:** Fabio scored 7 points less than 2 times the points Carlos scored. Fabio scored 31 points in the game. We need to find how many points Carlos scored. 2. **

1. **State the problem:** The price of apples increased by $0.75$ per pound. Sam bought $3$ pounds at the new price and paid a total of $5.88$. We need to find the original price p

1. **State the problem:** Floyd earns a base rate of 200 per month plus 12 for each album sold. Last month, he earned a total of 644. We need to find how many albums he sold. 2. **

1. **State the problem:** We are given that 64 is 4 times the difference between Sarah's age $a$ and 44, and Sarah is older than 44. 2. **Write the equation:** The difference betwe

1. **State the problem:** Simplify or analyze the expression $$x^2 - 1 + x \mid 2 - x$$. 2. **Interpretation:** The vertical bar \mid can mean different things depending on context

1. The problem is to simplify or analyze the expression given as $x^2 - 1 + x \mid 2 - x$. 2. The vertical bar $\mid$ can represent different operations depending on context, such

1. **State the problem:** Solve the quadratic equation $3x^2 + 2 = 11$ for $x$. 2. **Write the equation:**

1. مسئله: عبارت $x^2 - 1 + x$ را داریم و می‌خواهیم عدد سمت چپ را بر عدد سمت راست تقسیم کنیم به صورت تقسیم نردبانی. 2. ابتدا عبارت را مرتب می‌کنیم:

1. **State the problem:** We have the equation $y = 2x - 3$ and a table with some unknown values $a$ and $b$: | x | -1 | 0 | 1 | b | 3 |

1. **Problem Statement:** We have two problems to solve.

1. **Stating the problem:** We have a pattern of rhombuses arranged in rows with the number of rhombuses in each pattern given as 1, 3, 5, 7 for patterns 1, 2, 3, and 4 respectivel

1. **State the problem:** We need to find the value of $$\sqrt{x^2 + y^2}$$ when $$x = -3$$ and $$y = -4$$. 2. **Formula used:** The expression $$\sqrt{x^2 + y^2}$$ represents the

1. **State the problem:** We need to find the values of $x$ that must be excluded from the domain of the expression $$\frac{x}{3x^3 + 77}$$ because division by zero is undefined. 2

1. The problem states the inequality $x \leq 5$. 2. This means we are looking for all values of $x$ that are less than or equal to 5.

1. **Problem Statement:** Simplify and analyze the algebraic expression $$5x^3 - 7x^2 + 14 + 2x^3 - \frac{3x^4}{4}$$ and answer the following questions. 2. **Rewrite the expression

1. The problem asks to graph the inequality $x < -6$. 2. This inequality means all values of $x$ are less than $-6$, but do not include $-6$ itself.

1. **State the problem:** We need to evaluate the expression $$\frac{\sqrt{x^2}}{2} + \frac{3}{|y|}$$ when $$x = -2$$ and $$y = -3$$. 2. **Recall the formulas and rules:**

1. **Problem Statement:** Solve each linear equation for $x$ and identify the color code based on the answer. 2. **Formula and Rules:** For linear equations of the form $ax + b = c

1. **State the problem:** We need to divide the expression \(\frac{x^2 + 2xy - 8y^2}{x^2 + 2} \div (x^2 + 4xy)\). 2. **Rewrite division as multiplication:** Dividing by a term is t

1. **Problem 5.15:** Determine the value of the expression if $x = -1$. (Expression not explicitly given, assuming expression is $2$ as indicated.) Since the expression is $2$, its