🧮 algebra

1. **State the problem:** Onacha spent $\frac{1}{4}$ of his salary on food. From the remainder, he spent $\frac{3}{9}$ on school fees and the rest on leisure. His salary was 5400.

1. **State the problem:** We want to find the exact time between 10:00 and 11:00 such that six minutes from now, the minute hand is exactly opposite the position where the hour han

1. **State the problem:** We are asked to find a number such that when 18 is added to it and then 15 is subtracted, the result is 22. 2. **Set up the equation:** Let the number be

1. **State the problem:** Rationalize the denominator and simplify the expression $$\frac{14}{3-\sqrt{2}}$$. 2. **Formula and rule:** To rationalize a denominator with a binomial i

1. The problem is to solve a simple algebraic equation suitable for grade 7 level: Solve for $x$ in the equation $$3x + 5 = 20$$. 2. The formula used here is to isolate the variabl

1. **Problem statement:** Given the demand function $P = 190 - 0.6x$ and total cost function $TC = 40 + 30x + 0.4x^2$, where $P$ is price per unit and $x$ is units produced and sol

1. The problem is to explain the concept of standard form in mathematics. 2. Standard form can refer to different things depending on the context, but commonly it means writing num

1. **State the problem:** Rearrange the formula $$y=\frac{3a-2}{a-1}$$ to make $a$ the subject. 2. **Start by multiplying both sides by the denominator to eliminate the fraction:**

1. **State the problem:** Given the equation $$8x - \frac{2y}{3} = xy + y,$$ express $x$ in terms of $y$. 2. **Rewrite the equation:** Start by writing the equation clearly:

1. The problem asks to identify which inequality corresponds to the graph described. 2. The line crosses the y-axis at 5 and slopes downward, so the equation of the line is $y = -3

1. **State the problem:** Solve the equation $-3 = -4 + c$ for $c$. 2. **Isolate the variable:** To solve for $c$, add 4 to both sides of the equation to cancel out the $-4$ on the

1. **State the problem:** Solve the equation $-3 = -4 = c$ for $c$. 2. **Analyze the equation:** The equation $-3 = -4 = c$ is ambiguous because it suggests $-3 = -4$ and $-4 = c$

1. **State the problem:** Factorize the expression $54x^4 + 27x^3 a - 16x - 8a$. 2. **Group terms:** Group the expression into two parts to factor by grouping:

1. **State the problem:** Solve the quadratic equation formed by multiplying the binomials $\{5x-2\}$ and $\{2x-3\}$. This means we want to find $x$ such that $$(5x-2)(2x-3) = 0.$$

1. **State the problem:** Solve the quadratic equation $x^2 - 1x - 6 = 0$. 2. **Recall the quadratic formula:** For an equation $ax^2 + bx + c = 0$, the solutions are given by

1. **State the problem:** Solve the quadratic equation $$x(x-5)=0$$. 2. **Formula and rule:** The zero product property states that if $$ab=0$$, then either $$a=0$$ or $$b=0$$.

1. **Problem statement:** Calculate the value of $4.15$ multiplied by $50$ or $6$ using a scale factor. 2. **Formula:** To find the scaled value, use the multiplication formula:

1. **State the problem:** Solve the quadratic equation $x^2 - x = 0$. 2. **Formula and rules:** To solve quadratic equations, we can factorize the expression and use the zero produ

1. **State the problem:** Solve the quadratic equation $ (x-6)(x+3) = 0 $. 2. **Use the zero product property:** If the product of two factors is zero, then at least one of the fac

1. **State the problem:** Solve the equation $2(2x - 3) - (6x - 9) = 2x^2$ for $x$. 2. **Apply the distributive property:**

1. **State the problem:** Simplify the expression $\left(x-6\right)\left(x+3\right)$. 2. **Recall the distributive property (FOIL method):** When multiplying two binomials, multipl