🧮 algebra

1. **State the problem:** Solve the equation $7w = 35$ for $w$. 2. **Formula and rule:** To solve for $w$, divide both sides of the equation by 7, because dividing both sides by th

1. **State the problem:** Solve the system of equations by substitution: $$\begin{cases} y = 2x + 9 \\ y = 5x + 10 \end{cases}$$

1. **State the problem:** Solve the system of equations using the substitution method: $$\begin{cases} y = 3x + 1 \\ 3y - 5x = 11 \end{cases}$$

1. **State the problem:** Solve the equation $6w = -12$ for $w$. 2. **Formula and rules:** To solve for $w$, we use the rule of equality which states that if you perform the same o

1. **State the problem:** Solve the equation $-2 = -2t$ for the variable $t$. 2. **Recall the formula and rules:** To solve for $t$, we want to isolate $t$ on one side of the equat

1. **State the problem:** Solve the equation $-5y = -10$ for $y$. 2. **Formula and rules:** To solve for $y$, we need to isolate $y$ on one side of the equation. Since $y$ is multi

1. **State the problem:** Solve the equation $-12r = 12$ for $r$. 2. **Formula and rules:** To solve for $r$, we need to isolate $r$ on one side of the equation. Since $r$ is multi

1. Stating the problem: Calculate the value of $7 \times \left( \frac{3}{4} \right) - \left( \frac{2}{5} \right)$.\n\n2. Use the distributive property and order of operations. Firs

1. **State the problem:** We are given the expression $5(7 + 2x)$ and its transformations in subsequent lines. We need to identify the property that justifies each step. 2. **Step

1. **State the problem:** Find the equation of the tangent line to the curve defined by $$ (x^2 + x^2)^3 = 8x^2y^2 $$ at the point $(-1, 1)$. 2. **Simplify the equation:** Note tha

1. **State the problem:** We are asked to find the matrix $A$ given by $$A = \begin{pmatrix} 3 & 9 \\ 4 & 3 \end{pmatrix} - \begin{pmatrix} 5 & 5 \\ 4 & 3 \end{pmatrix}$$

1. The problem states: "Three more than 7 times a number is the same as 208 more than twice the number." We need to write an equation using $x$ to represent this sentence and then

1. **State the problem:** Calculate $20^2$. 2. **Formula used:** The expression $a^b$ means $a$ multiplied by itself $b$ times.

1. **State the problem:** Maria is monitoring two substances with temperatures changing over time. Substance A starts at 97.7 degrees and increases by 1.1 degrees per minute. Subst

1. **State the problem:** The problem says "The difference of a number and 14 is equal to 48." We need to write an equation using $x$ to represent this and then solve for $x$. 2. *

1. **Problem 1:** Solve for $x$ in the equation $$2 \log_9(\sqrt{x}) - \log_9(6x - 1) = 0.$$ 2. **Problem 2:** Solve for $x$ in the equation $$\log_8(7x + 5) - \log_8(x - 10) = \lo

1. The problem states: The sum of a number and 18 is equal to 42. 2. Let the number be $x$. The phrase "sum of a number and 18" translates to $x + 18$.

1. **State the problem:** Simplify the expression $$\frac{(n+1)^2 + 1}{2 (n+1)^2} - \frac{n^2 + 1}{2 n^2}$$. 2. **Write the expression clearly:**

1. **State the problem:** We are given a 2x2 matrix \( \begin{pmatrix} 2 & 4 \\ 5 & 1 \end{pmatrix} \) and asked to find the value of \( x \) associated with its determinant. 2. **

1. The problem states: The product of a number and 14, increased by 28 is 98. 2. Let the number be $x$. The product of the number and 14 is $14x$.

1. The problem is to graph the function $f(x) = |x|$ and determine if it is continuous everywhere. 2. The absolute value function is defined as: