🧮 algebra

1. **State the problem:** Solve the inequality $4x + 4y \le 24$ for $y$ in terms of $x$. 2. **Rewrite the inequality:** We want to isolate $y$ on one side.

1. Problem: Factorise the following expression using the cross method: $d(d - 5) - 84$. 2. Expand to standard quadratic form.

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

1. Problem: Divide the polynomial $6x^5 - x^4 + 4x^3 - 5x^2 - x - 15$ by $2x^2 - x + 3$. 2. Formula and rules: Use polynomial long division: repeatedly divide the leading term of t

1. **State the problem:** Solve for $x$ in the equation $$(6 - \sqrt{35})^x + (6 + \sqrt{35})^x = 142.$$\n\n2. **Recognize the form:** Let $a = 6 - \sqrt{35}$ and $b = 6 + \sqrt{35

1. Problem: Simplify the expression $\frac{1}{y^2+3y+2} \div \frac{2}{y^2-4}$. 2. Formula and rule: To divide fractions use the rule $\frac{a}{b} \div \frac{c}{d} = \frac{a}{b} \cd

1. **State the problem:** Simplify the expression $$\frac{1}{y^{2} + 3y + 2} \div \frac{2}{y^{2} - 4}$$. 2. **Recall the division rule for fractions:** Dividing by a fraction is th

1. **State the problem:** Solve the system of equations using the substitution method: $$4x + y = 17 \quad (1)$$

1. **State the problem:** Solve the system of linear equations using the substitution method: $$4x + y = 17 \quad (1)$$

1. Simplify the expression \( \frac{12 a^0 b^3 c^{-1}}{15 a^{-2} b^5 c^{-3}} \). 2. Simplify the expression \( \frac{(3 x y^{-2})^{-2}}{3 x^{-2} y} \).

1. **State the problem:** Evaluate and express in standard form the sum $$(7.01 \times 10^6) + (5 \times 10^5).$$ 2. **Recall the rule:** To add numbers in scientific notation, the

1. Simplify the expression \(\frac{12a^0 b^3 c^{-1}}{15 a^{-2} b^5 c^{-3}}\). 2. Simplify the expression \(\frac{(3xy^{-2})^{-2}}{3x^{-2} y}\).

1. **Stating the problem:** We are given a sequence where the number of small triangles for Figure 1 is 4, and for Figure 2 is 9. We need to find the number of small triangles for

1. **State the problem:** Evaluate $$\frac{(5 \times 10^{3}) \times (2 \times 10^{-3})}{7}$$ and express the answer in standard form rounded to 2 decimal places. 2. **Use the prope

1. **State the problem:** Simplify the expression $$\frac{(3xy^{-2})^{-2}}{3x^{-2}y}$$. 2. **Recall the rules:**

1. **Énoncé du problème :** Trouver pour quelles valeurs de $x$ la fonction $F(x) = \frac{A(x)}{B(x)}$ existe. 2. **Rappel important :** Une fonction rationnelle $F(x) = \frac{A(x)

1. **State the problem:** Simplify the expression $$\frac{(3xy^{-2})^{-2}}{3x^{-2}y}$$. 2. **Recall exponent rules:**

1. **Problem:** Given two numbers A and B with ratio 3:5 and their sum is 160, find B. 2. **Formula:** If $A:B=3:5$, then $A=3x$ and $B=5x$ for some $x$.

1. The problem is to evaluate the expression $23 - 24$. 2. The subtraction operation means we take 24 away from 23.

1. The problem is to simplify the expression \( \sqrt{x} \), which means finding the principal square root of \( x \). 2. The square root function is defined as \( \sqrt{x} = y \)

1. **State the problem:** Check if the points (1, 2) and (4, 0) are solutions of the equation $x - 2y = 4$. 2. **Recall the rule:** A point $(x, y)$ is a solution to the equation i