🧮 algebra

1. **State the problem:** Solve the equation $$|4x - 5| = |x - 1|$$ for $x$. 2. **Recall the property of absolute values:** For any real numbers $A$ and $B$, if $$|A| = |B|,$$ then

1. **Problem:** Calculate $12 - \left(\frac{8}{5} + 3 \div \frac{2}{3}\right)$ using BODMAS rules. 2. **Step 1:** Understand BODMAS (Brackets, Orders, Division/Multiplication, Addi

1. The problem is to simplify the expression $12 - \left( \frac{8}{5} + 3 \div \frac{2}{3} \right)$. 2. Recall the order of operations: parentheses first, then division and multipl

1. The problem is to simplify the expression $5x^2 + 5x$. 2. We use the distributive property which states that $a(b + c) = ab + ac$.

1. **State the problem:** Expand and simplify the expression $5x(x+1)$. 2. **Formula used:** Use the distributive property $a(b+c) = ab + ac$.

1. **State the problem:** Expand and solve the equation $5x(x-1) = 0$. 2. **Expand the expression:** Use the distributive property $a(b+c) = ab + ac$.

1. The problem involves understanding the correct direction of operations for four machines that transform input values to output values. 2. Machine 1 adds 8 to the input to get th

1. **Problem Statement:** A toy is sold for 220 with a profit rate of 10% on the cost price. We need to find the cost price. 2. **Formula:** Profit percentage is given by

1. The problem is to simplify the expression $5x - 5x$. 2. The formula used here is the distributive property and combining like terms: $a x - a x = (a - a) x = 0 \cdot x = 0$.

1. The problem is to solve the system of 8 simultaneous linear equations with 8 variables. 2. The general form of a system of linear equations is:

1. **State the problem:** Given $a = 1 + \frac{1/2024}{2025}$ and $b = 1 + \frac{1/2025}{2026}$, find the value of $$\frac{a+b}{\frac{1}{a} + \frac{1}{b}}.$$\n\n2. **Rewrite $a$ an

1. **State the problem:** We are given a function defined as $f(5x) = \frac{5}{2 + x}$ and asked to find the value of $f(-5)$. 2. **Understand the function:** The function is given

1. The problem is to solve the equation $2x + 3 = 11$ for $x$. 2. We use the basic algebraic principle: to isolate $x$, perform inverse operations to both sides of the equation.

1. The problem is to solve the equation $2x + 3 = 11$ for $x$. 2. The formula used here is to isolate $x$ by performing inverse operations. We subtract 3 from both sides to get rid

1. The problem is to solve the equation $2x + 3 = 11$ for $x$. 2. We use the basic algebraic principle: to isolate $x$, perform inverse operations to both sides of the equation.

1. The problem is to solve the equation $2x + 3 = 11$ for $x$. 2. We use the basic algebraic principle: to isolate $x$, perform inverse operations.

1. **State the problem:** Given $x = -1234567$, find the value of the expression

1. **State the problem:** Find how many trailing zeroes are in the product $$650 \times 4^6 \times 5^9$$. 2. **Recall the rule for trailing zeroes:** Trailing zeroes in a number co

1. **Problem Statement:** We have four inverse function machines:

1. **Énoncé du problème :** Calculer $AB$ et $A^2 + B^2$ avec

1. **State the problem:** Find the sum of all even numbers from 5 to 15. 2. **Identify the even numbers in the range:** The even numbers between 5 and 15 are 6, 8, 10, 12, and 14.