🧮 algebra

1. **Stating the problem:** Solve the equation $$\frac{2x+3}{x-1} = 4$$ for $x$.

1. **State the problem:** We have an account with an initial investment of $1 that pays 150% interest per month but also charges a fixed fee of 3 per month. We want to find the val

1. **State the problem:** Solve the equation $$45(p^2 - 1) = 56p$$ for $p$. 2. **Expand and rearrange the equation:**

1. **State the problem:** Find the value of the inverse function $f^{-1}(3)$ given $f(x) = 2x - 1$. 2. **Recall the formula for inverse functions:** To find $f^{-1}(y)$, solve the

1. **State the problem:** Simplify the expression $$\frac{(-6x^{2})^{3}}{(3x^{-4})^{2}}$$. 2. **Apply the power of a product rule:** For any numbers $a$ and $b$, and exponent $n$,

1. **State the problem:** Solve for $h$ in the equation $$-100 = -4(h + 92)$$. 2. **Use the distributive property:** Multiply $-4$ by each term inside the parentheses:

1. **State the problem:** Simplify the expression $$\frac{2x^{-2} y^{-2}}{16x^{-12} y^2}$$. 2. **Recall the rules:**

1. The problem asks to find $f^{-1}(5)$ where $f(x) = x^2 + 1$. 2. The function $f(x) = x^2 + 1$ maps $x$ to $x^2 + 1$. The inverse function $f^{-1}(y)$ gives the value of $x$ such

1. **State the problem:** Solve the two-step equation $$-7 + -7c = 49$$ for $$c$$. 2. **Add 7 to both sides** to isolate the term with $$c$$:

1. **Problem:** Solve the inequality $$12 < p + 6$$. 2. **Formula and rules:** To solve inequalities, isolate the variable on one side by performing inverse operations. Remember, w

1. **Stating the problem:** We want to learn how to add and subtract positive and negative numbers. 2. **Important rules:**

1. Let's start by understanding what an equation is: an equation is a mathematical statement that shows that two expressions are equal, often containing an unknown variable $x$ tha

1. **State the problem:** We are given the first term $a_1 = -20$ of an arithmetic sequence and the fourth term $a_4 = -2$. We need to find the eighth term $a_8$. 2. **Recall the f

1. The problem is to calculate $\frac{9}{10} \times 44$. 2. The formula for multiplying a fraction by a whole number is:

1. The problem is to calculate $\frac{9}{10} \times 44$. 2. The formula for multiplication of a fraction by a whole number is:

1. Let's start by stating the problem: We want to describe the algebraic equation $10x - 49 = 51$ using a real-life situation. 2. The equation $10x - 49 = 51$ means that if you tak

1. **State the problem:** (a) Find the greatest common factor (GCF) of 2 and 6.

1. **State the problem:** (a) Find the greatest common factor (GCF) of 2 and 6.

1. **State the problem:** Solve the compound inequality $x - 6 < -9$ and $-1 + x \geq -7$. 2. **Solve each inequality separately:**

1. **State the problem:** We want to graph the region containing all points $(x,y)$ such that $2x + y < 3$. 2. **Rewrite the inequality:** To graph this, first express $y$ in terms

1. The problem asks to translate the expression \textit{a (b+c)} into an algebraic expression. 2. The expression \textit{a (b+c)} means that the variable $a$ is multiplied by the s