🧮 algebra

1. Let's solve a simple algebra problem suitable for Year 6 learners: Find the value of $x$ in the equation $2x + 3 = 11$. 2. The formula we use here is to isolate $x$ by performin

1. **State the problem:** We know that 50% of the children in the sports club go swimming, and 50% of those who swim also dive. We are told that 5 children both swim and dive. We n

1. **Problem:** Find the distinct roots of the quadratic equation $x^2 - 5x + 6 = 0$. 2. **Formula:** For a quadratic equation $ax^2 + bx + c = 0$, the roots are given by the quadr

1. **Problem Statement:** Find the value of the constant $k$ in the first table where $x$ and $f(x)$ values are given as: $$\begin{array}{c|c}

1. **State the problem:** Calculate the total daily wages paid by the factory. 2. **Write the expression:** Total wages = (Number of workers at 150 per day) \times 150 + (Number of

1. **State the problem:** We need to find the height of the NASA Space Shuttle's external tank. The height is calculated by adding 4 to the width and then multiplying by 8. The sum

1. Let's start by clarifying the problem you want to solve. Since you mentioned "that question" without specifying, I'll assume you want a general example of solving an algebraic e

1. **State the problem:** Solve the system of linear equations: $$0.08x + 0.15y = -0.76$$

1. **State the problem:** We need to find the height of the NASA Space Shuttle's external tank. The height is calculated by adding 4 to the width and then multiplying by 8. The sum

1. **State the problem:** We have two phone plans with different cost structures. We want to find the number of minutes where the total cost of Plan A equals the total cost of Plan

1. **State the problem:** We have two phone plans with different cost structures. Plan A costs $21 plus $0.13 per minute, and Plan B costs $0.17 per minute with no initial fee. We

1. The problem asks to write the expression $-x^{1/3} + \frac{9}{7} \cdot 2$ as one fraction with positive exponents. 2. First, simplify the constant multiplication: $\frac{9}{7} \

1. **State the problem:** A science class has 45 students total. The number of males is 13 more than the number of females. We need to find how many males and females are in the cl

1. **State the problem:** We know that 40% of a Fermium-256 sample has decayed, and 53 grams remain. We need to find the original mass of the sample. 2. **Understand the problem:**

1. **State the problem:** Solve the system of linear equations: $$-\frac{1}{3}x + \frac{1}{2}y = 14$$

1. The problem is to show that two expressions are equal by solving one and demonstrating it results in the other, and vice versa. 2. To prove two expressions are equal, we can sol

1. **State the problem:** Simplify the expression $$x^{\frac{2}{5}} \left(x^{\frac{6}{5}} - x^{\frac{7}{2}}\right)$$ and express the answer with positive exponents. 2. **Recall the

1. **State the problem:** Solve for $x$ in the equation $$\frac{6.11 + x}{5} = 152.4.$$\n\n2. **Formula and rules:** To solve for $x$, multiply both sides of the equation by 5 to e

1. **State the problem:** We have two systems of linear equations and need to determine the nature of their solutions (no solution, unique solution, or infinitely many solutions).

1. **State the problem:** We are given two purchases with amounts of trail mix and jelly beans and their total costs. We want to find the cost per pound of trail mix ($x$) and jell

1. **State the problem:** We need to find the cost of coating a rectangular driveway that measures 15 feet by 20 feet, with a coating cost of 3.00 per square foot. 2. **Formula use