🧮 algebra

1. **State the problem:** Simplify the expression $8y + 6x - 4y$. 2. **Identify like terms:** Terms with the same variable can be combined. Here, $8y$ and $-4y$ are like terms, whi

1. **State the problem:** We need to find the total cost of 3 pens and 2 boxes. 2. **Given information:**

1. **State the problem:** Find the rate of interest per annum when the simple interest (SI) on 800 for 3 years is 54. 2. **Formula for simple interest rate:**

1. **Nêu bài toán:** Cho đa thức $M = 3x^{2}y - 2xy + 3$ và $N = x^{2}y + xy - 3$. Tính đa thức $P = M + N$ và giá trị của $P$ khi $x = -4$ và $y = 2$. 2. **Công thức và quy tắc:**

1. **State the problem:** Solve the inequality \(\left|\frac{1}{2}w - \frac{3}{4}\right| < 2\). 2. **Recall the rule for absolute value inequalities:**

1. **Problem Statement:** Michelle bought 20 jars for 3500 with a 15% discount and sold 10 jars for 1800 and the remaining 10 jars at 185 each. Find the profit percent. 2. **Formul

1. **Problemstellung:** Wir sollen den Schnittpunkt der Graphen von $f(x) = x^2$ und $g(x) = 4x - 4$ berechnen. 2. **Formel und Vorgehen:** Der Schnittpunkt zweier Funktionen liegt

1. **Problemstellung:** Berechne die Schnittpunkte der Graphen von $$f(x) = x^2 - 3x + 7$$ und $$g(x) = x + 2$$. 2. **Gleichung aufstellen:** Die Schnittpunkte liegen dort, wo $$f(

1. **State the problem:** Solve for $a$ in the equation $$4a + 5 = 2 + 3.25a$$. 2. **Write down the formula and rules:** To solve for $a$, we need to isolate $a$ on one side of the

1. **State the problem:** Solve for $d$ in the equation $$6d - \frac{11}{2} = 2d - \frac{13}{2}$$. 2. **Isolate the variable terms on one side:** Subtract $2d$ from both sides to g

1. The problem is to analyze the linear function $y = x + 4$. 2. The formula for a linear function is $y = mx + b$, where $m$ is the slope and $b$ is the y-intercept.

1. The problem asks to express a set in both interval notation and set builder notation. 2. Interval notation describes all numbers between two endpoints, using brackets [ ] for in

1. **State the problem:** We are given the quadratic function $y = -2(x+4)^2 - 1$ and want to analyze it. 2. **Formula and rules:** This is a quadratic function in vertex form $y =

1. **State the problem:** Evaluate $\{x \mid x=4\}$. 2. **Use the definition of set-builder notation:** This means “the set of all $x$ such that $x=4$.”

1. **State the problem:** We need to find the average score of Alice, Chris, Dan, and Emeril from their golf scores. 2. **List the scores:**

1. The problem is to simplify the expression $-i^2$. 2. Recall that $i$ is the imaginary unit defined by the property $i^2 = -1$.

1. The problem asks to find the reciprocal of the number $\frac{1}{14}$. 2. The reciprocal of a number $x$ is defined as $\frac{1}{x}$. This means you flip the numerator and denomi

1. **State the problem:** We need to find a number such that the difference between the number and 9 equals 37 less the number. 2. **Set up the equation:** Let the number be $x$. T

1. **State the problem:** We need to perform the subtraction \( \frac{1}{7} - \frac{1}{11} \) and simplify the answer. 2. **Formula and rules:** To subtract fractions, we find a co

1. **State the problem:** Amy charges 65 per student for a 6-week session and collects a total of 1690 from one group. We need to find the number of students in that group. 2. **Fo

1. **State the problem:** Simplify the expression $$-7 + (19)(9) + 2$$. 2. **Recall the order of operations:** Multiplication comes before addition and subtraction.