🧮 algebra

1. **State the problem:** Solve the system of equations: $$\begin{cases} x - 8y = -17 \\ x + y = 10 \end{cases}$$

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

1. **Problem statement:** We need to create a linear inequality representing the total number of participants for yoga and spin classes, given the constraints. Define variables:

1. **State the problem:** Simplify the expression $\frac{2}{5} \times \frac{7}{6}$.\n\n2. **Formula used:** When multiplying fractions, multiply the numerators together and the den

1. The problem is to multiply the fractions $\frac{9}{4}$ and $\frac{4}{3}$.\n\n2. The formula for multiplying fractions is:\n$$\frac{a}{b} \times \frac{c}{d} = \frac{a \times c}{b

1. **State the problem:** Factor the expression $5p^3 - 20p^2 + 5p^3 + 20p^2$ by grouping. 2. **Combine like terms:** First, combine the terms with the same powers of $p$.

1. **State the problem:** We need to find the sum of the fractions $\frac{3}{8} + \frac{7}{3} + \frac{5}{4}$.\n\n2. **Formula and rules:** To add fractions, they must have a common

1. **State the problem:** Simplify the expression $2 \frac{4}{15} - \frac{5}{6}$. 2. **Convert the mixed number to an improper fraction:**

1. **State the problem:** Calculate the value of $3 \frac{1}{15} - \frac{3}{8}$. 2. **Convert the mixed number to an improper fraction:**

1. **State the problem:** Add the fractions $\frac{2}{3}$, $\frac{5}{4}$, and $\frac{7}{6}$. 2. **Formula and rules:** To add fractions, find a common denominator, then add the num

1. **State the problem:** We need to find the sum of the fractions $\frac{9}{4} + \frac{1}{8} + \frac{2}{5}$.\n\n2. **Find a common denominator:** The denominators are 4, 8, and 5.

1. **State the problem:** Solve the system of equations: $$4x - y = -1$$

1. **State the problem:** We are given two functions $f(x)=6x-2$ and $g(x)=2x+8$. We need to find the value of $x$ such that $f(x)=16$. 2. **Write the equation:** Since $f(x)=16$,

1. **State the problem:** We are given two functions $f(x) = 6x - 2$ and $g(x) = 2x + 8$. We need to calculate the value of the composite function $fg(-4)$, which means $f(g(-4))$.

1. The problem asks to calculate the composition of functions $f$ and $g$, denoted as $fg(x)$, which means $f(g(x))$. 2. The formula for composition is $fg(x) = f(g(x))$, meaning w

1. Let's start by understanding the problem: we have three expressions to simplify or evaluate: - $4 - \frac{5}{6}$

1. **State the problem:** We have a rectangular rug with length $3$ feet and width $2.5$ times the length. We need to find the width. 2. **Formula:** Width $= 2.5 \times$ Length

1. **State the problem:** We need to find the length of a billboard given its area and width. 2. **Given:**

1. **State the problem:** We need to find the value of the expression $$7x^2 - 2x + 2$$ when $$x = 3$$. 2. **Recall the formula:** The expression is a quadratic polynomial in terms

1. The problem is to evaluate the expression $-\left|15 + 6\right| + (-3)$.\n\n2. Recall that the absolute value $|x|$ of a number $x$ is the distance from zero on the number line,

1. **State the problem:** Calculate the value of the expression $$17 + 3 | -5 + (-2) |$$. 2. **Understand the absolute value:** The absolute value of a number is its distance from