🧮 algebra

1. **State the problem:** We need to find the value of $x$ in the equation $103x = 67$. 2. **Formula and rules:** To solve for $x$, we use the rule of division to isolate $x$ by di

1. **State the problem:** Solve the linear equation $4x + 3 = 1 - 2x$ for $x$. 2. **Write down the formula and rules:** To solve for $x$, we want to isolate $x$ on one side of the

1. **State the problem:** Solve the inequality $$2x^2 - 3x - 16 > 5 - 2x$$ for $x$. 2. **Rewrite the inequality:** Move all terms to one side to set the inequality to zero:

1. The problem is to find the 29th term in the Fibonacci sequence. 2. The Fibonacci sequence is defined by the recurrence relation:

1. **State the problem:** We need to find the value of $x$ in the equation $103^x = 67$ where the base is 10. 2. **Formula and rules:** To solve for $x$ when the variable is in the

1. **State the problem:** Solve the equation $7(7-x)=6+2x$ for $x$. 2. **Apply the distributive property:** Multiply 7 by each term inside the parentheses.

1. **State the problem:** Factorise completely the expression $6x^2 + 25 - 9$. 2. **Simplify the expression:** Combine like terms $25 - 9$.

1. **State the problem:** We are given data for distance traveled (in km) and corresponding fare (in AED) and need to construct a linear function that models this relationship. 2.

1. **State the problem:** We have 17 squirrels sitting on 4 trees. Each tree has at least 2 squirrels.

1. **State the problem:** We need to determine which inequality corresponds to the solution set shown on the graph. The graph shows an open circle at $-2$ and shading to the right,

1. **Problem statement:** Alex threads white and black beads alternately onto a string. Two groups of 5 beads each are hidden (covered). We need to find how many white beads are hi

1. **State the problem:** Jessica is building a model skyscraper with each floor 4 inches tall and an 8-inch spire on top. The total height must be at least 50 inches. We need to f

1. The problem is to analyze the linear equation $y = 2x - 1.5$ and understand its properties. 2. The general form of a linear equation is $y = mx + b$, where $m$ is the slope and

1. The problem asks which table shows a proportional relationship between weight and price. 2. A proportional relationship means the ratio between weight and price is constant.

1. **State the problem:** We are given the polynomial function $P(x) = x^2 + x + 2$ and asked to find the value of $P(0)$. 2. **Recall the formula:** To find $P(0)$, substitute $x

1. The problem states that $(f \circ g)(0) = 2$, which means $f(g(0)) = 2$. 2. From the graph, observe the function $g(x)$, which is a downward-opening parabola intersecting the y-

1. **State the problem:** Solve the system of linear equations: $$\begin{cases}7x + 2y = 24 \\ 8x + 2y = 30\end{cases}$$

1. **State the problem:** A photograph scale shows that every $1 \frac{1}{4}$ inches represents 100 yards in real life. The mountain height in the photo is 8 inches. Find the actua

1. Énonçons le problème : Résoudre l'équation $$x + 1 + \sqrt{x} - 1 = 0$$. 2. Simplifions l'équation en combinant les termes constants : $$x + \sqrt{x} + (1 - 1) = 0 \Rightarrow x

1. **State the problem:** Solve the equation $\sqrt{6x+7} = 2$ for $x$. 2. **Recall the formula and rules:** To solve an equation involving a square root, we isolate the square roo

1. **State the problem:** Simplify the expression $\left(\frac{5}{x}\right)^6 \left(\frac{1}{x}\right)^3$ using properties of exponents and write it in radical form. 2. **Recall th