🧮 algebra

1. **State the problem:** Simplify the expression $$\frac{2x^2 - 8}{4x}$$. 2. **Recall the formula and rules:** To simplify a rational expression, factor numerator and denominator

1. **State the problem:** Factor the quadratic expression $3x^2 + 5x - 12$. 2. **Recall the factoring formula:** For a quadratic $ax^2 + bx + c$, we look for two numbers that multi

1. **State the problem:** Simplify or analyze the polynomial expression $3x^3 - x^2 + 6x - 2$. 2. **Identify the polynomial:** This is a cubic polynomial of the form $ax^3 + bx^2 +

1. **State the problem:** Solve the equation $x\sqrt{2} = 7\sqrt{2}$ for $x$. 2. **Formula and rules:** To solve for $x$, we want to isolate $x$ on one side of the equation. Since

1. Let's identify the coefficients $a$, $b$, and $c$ in the quadratic equation $3x^2 + 6x - 24 = 0$. 2. The general form of a quadratic equation is $ax^2 + bx + c = 0$.

1. **State the problem:** A human and a turtle compete in a 1 km race. The turtle moves at a constant speed of 0.2 km/h and receives a 980 m head start. The human runs at a speed 1

1. **State the problem:** Solve the equation $$\frac{5^{3-y}}{\pi} = 2$$ for $y$. 2. **Isolate the exponential term:** Multiply both sides by $\pi$ to get rid of the denominator.

1. **State the problem:** Solve the linear equation $4x - 2y + 3 = 0$ for $y$ in terms of $x$. 2. **Rewrite the equation:** We want to isolate $y$ on one side. Start by moving othe

1. **State the problem:** Given that $HI = 10$ and $IE = x - 4$, find the value of $x$ and then find $IE$. 2. **Understand the relationship:** Since $HI$ and $IE$ are parts of a se

1. **State the problem:** Solve the linear equation $y - 3x - 1 = 0$ for $y$. 2. **Rewrite the equation:** The equation is given as $y - 3x - 1 = 0$.

1. The problem is to determine if the inequality $22 \ge 55$ is true or false. 2. The symbol $\ge$ means "greater than or equal to." So, we are checking if 22 is greater than or eq

1. Let's start with a simple algebra problem suitable for grade 9 students: Solve for $x$ in the equation $2x + 3 = 11$. 2. The formula we use here is to isolate $x$ by performing

1. The problem is to understand the concept of functions in mathematics. 2. A function is a relation between a set of inputs and a set of possible outputs where each input is relat

1. **State the problem:** Simplify the expression $x + 527$. 2. **Understand the expression:** This is a simple algebraic expression consisting of a variable $x$ and a constant $52

1. The problem asks to identify the correct graph for the inequality $y < \frac{1}{2}x - 4$. 2. The inequality is linear and in slope-intercept form $y < mx + b$ where $m = \frac{1

1. **State the problem:** Solve the inequality $x + 5 > 7$. 2. **Isolate the variable:** To solve for $x$, subtract 5 from both sides of the inequality.

1. **State the problem:** Find the equation of the line passing through points $(2, -3)$ and $(4, 2)$ in standard form. 2. **Formula for slope:** The slope $m$ of a line through po

1. The problem asks to identify the correct graph of the linear equation $$y + 3 = -\frac{1}{2}(x - 4)$$. 2. First, rewrite the equation in slope-intercept form $y = mx + b$ to und

1. **State the problem:** Find the correct equation(s) of the line passing through the point $(-1,4)$ with slope $m = -3$. 2. **Formula used:** The point-slope form of a line is

1. **State the problem:** Rewrite the linear equation $y - 5 = 3(x + 1)$ in slope-intercept form, which is $y = mx + b$ where $m$ is the slope and $b$ is the y-intercept. 2. **Use

1. The problem states that a consultant needs to make at least 720 this week. 2. She earns 120 for each new written piece (let's call the number of new pieces $x$) and 60 for each