🧮 algebra

1. **State the problem:** Solve the compound inequality $$y - 20 \geq -9 \text{ or } y - 5 \leq 2$$ and graph the solution on a number line. 2. **Solve each inequality separately:*

1. **State the problem:** Solve the compound inequality $$6 > g - 14 \geq 3$$ for $g$ and graph the solution on a number line. 2. **Understand the compound inequality:** This means

1. **State the problem:** Solve the compound inequality $$m + 8 \leq 8 \text{ or } m + 3 \geq 12$$ and graph the solution. 2. **Solve each inequality separately:**

1. **State the problem:** Solve the compound inequality $$m + 8 \leq 8 \text{ or } m + 3 \geq 12$$ and graph the solution on a number line. 2. **Solve each inequality separately:**

1. **State the problem:** Solve the compound inequality $$v - 20 \geq -5 \text{ or } v - 15 < -3$$ and graph the solution on a number line. 2. **Solve each inequality separately:**

1. **State the problem:** Find the least common multiple (LCM) of the polynomials $9(x + 2)(2x - 1)$ and $3(x + 2)$.\n\n2. **Recall the formula and rules:** The LCM of two polynomi

1. **State the problem:** Solve the equation $12 + 2d = 4d - 8$ for $d$. 2. **Write down the equation:**

1. **State the problem:** Mason owns 48 books in total. Hanna owns 6 times as many non-fiction books as Mason. We need to find how many books Hanna owns in total. 2. **Analyze Maso

1. Solve for $x$ in the equation $x - 5 = -8$. $$x - 5 = -8$$

1. Problem: Given $x - 5 = -8$, evaluate $(x^2 - 5)(x^{-3} - x)$. 2. First, solve for $x$:

1. The problem asks if the relationship between $x$ and $y$ in the table is proportional and to find the constant of proportionality if it exists. 2. A proportional relationship me

1. **State the problem:** Simplify the expression $24y^2 + 16y$ by factoring. 2. **Recall the factoring formula:** To factor an expression, find the greatest common factor (GCF) of

1. **State the problem:** Expand and fully simplify the expression $$(2x - 1)(x - 5)(x + 6)$$. 2. **Use the distributive property (FOIL for binomials) step-by-step:** First, multip

1. **Stating the problem:** We want to find a formula for the number of matches $T_n$ used to make $n$ hexagons joined side-by-side, where each additional hexagon shares one match

1. **State the problem:** Solve the inequality $$\frac{3}{x-4} \leq \frac{2}{x-3}$$ for $x$. 2. **Rewrite the inequality:** Bring all terms to one side:

1. **Problem a:** Prove by mathematical induction that $$2 + 7 + 12 + \cdots + (5n - 3) = \frac{n}{2}(5n - 1)$$ for all positive integers $n$. 2. **Base case:** For $n=1$, the left

1. **State the problem:** Solve the equation $$\frac{7}{3x + 1} = \frac{2}{x + 2}$$. 2. **Use the cross-multiplication method:** When two fractions are equal, their cross products

1. The problem is to solve the equation of everything, which is not a specific mathematical equation. 2. To solve an equation, we need a clear expression or formula.

1. **Identify the domain and range of** $y=\sqrt{x-2}+5$. 2. **Domain**: The expression inside the square root must be non-negative.

1. **State the problem:** We are given the function $f(t) = 243 \left(\frac{3}{5}\right)^t$ which models the number of stray cats $t$ years after an animal control program started.

1. **State the problem:** We need to find the percentage increase in the price of a sofa that was originally 540 and increased by 135. 2. **Formula for percentage increase:**