🧮 algebra

1. **State the problem:** Solve the equation $$\frac{4x-3}{x+3} + 1 = \frac{3x+1}{x+3}$$. 2. **Rewrite the equation:** To work with a common denominator, express 1 as $$\frac{x+3}{

1. **State the problem:** Solve the equation $$\frac{7-n}{9-2n} = 1$$. 2. **Recall the formula and rules:** To solve an equation with a fraction equal to a number, multiply both si

1. **State the problem:** We want to find how long it takes for Rip van Winkle's beard to grow by 5 millimeters based on the graph showing beard length over time. 2. **Identify poi

1. **State the problem:** We need to find the slope of a line that crosses the y-axis at $ (0, 2) $ and the x-axis at $ (1.5, 0) $. 2. **Recall the formula for slope:** The slope $

1. **State the problem:** We need to find the slope of a line passing through the points approximately $(-4, 3)$ and $(4, -3)$. 2. **Formula for slope:** The slope $m$ of a line pa

1. The problem asks for the slope of a line given its graph. 2. The slope formula for a line passing through two points $ (x_1, y_1) $ and $ (x_2, y_2) $ is:

1. **State the problem:** We need to find the slope of the line passing through the points $(0,0)$, $(1,2)$, and $(2,4)$. 2. **Formula for slope:** The slope $m$ of a line passing

1. **State the problem:** We need to find the slope of a line that crosses the x-axis at approximately $(-2, 0)$ and the y-axis at approximately $(0, -2)$. 2. **Recall the formula

1. **State the problem:** We need to find the slope of a line passing through the points $(-1, 4)$ and $(0, 2)$. 2. **Formula for slope:** The slope $m$ of a line passing through p

### Question One 1. **Problem Statement:**

### Question One 1. **Problem Statement:**

1. The problem asks to convert percentages to decimal form rounded to 2 decimal places. 2. The formula to convert a percentage to a decimal is $$\text{Decimal} = \frac{\text{Percen

1. **State the problem:** We need to find the result of the expression $(+9)-(+4)$. 2. **Recall the rule for subtraction of signed numbers:** Subtracting a positive number is the s

1. Let's look at the problem: we want to understand the expression $x^2 + 7x + 12$. 2. This is a quadratic expression, which means it has a term with $x^2$, a term with $x$, and a

1. **State the problem:** Solve the equation $x+5=7$ for $x$. 2. **Formula and rules:** To isolate $x$, subtract $5$ from both sides of the equation.

1. **Problem Statement:** Solve the equations in 3(a) and evaluate the expressions in 4(a). ---

1. The problem asks to sketch the graphs of $Q(x)=2.W(x)$, $R(x)=-W(x)$, and $S(x)=-2.W(x)$ given the graph of $F(x) = 2x^3 - 3x^2 + 1$. 2. First, we need to understand what $W(x)$

1. **Problem:** Determine if the point $(4, -2)$ satisfies the inequality $y > x^2 - 7x - 9$. 2. **Formula:** Substitute $x=4$ and $y=-2$ into the inequality.

1. **State the problem:** Simplify and solve the equation $$2+3\cdot(-2-28x)+ x5=2-x-4+23 \cdot(x+3)$$ for $x$. 2. **Rewrite the equation clearly:**

1. The problem gives two functions: $$y = (x-1)^3 + 5$$ and $$y = -(x+7)^4$$. 2. These are polynomial functions: the first is a cubic function shifted right by 1 and up by 5, the s

1. **Problem 1: Calculate the cost price and selling price of articles with given profit percentages.** 2. Given: