🧮 algebra

1. Let's create a simple linear equation that is easy to fit on a cue card. 2. A linear equation has the form $$y = mx + b$$ where $m$ is the slope and $b$ is the y-intercept.

1. **State the problem:** Calculate $\left(7 \frac{5}{12} - 5 \frac{3}{4}\right) \div 2^{2 \frac{1}{2}}$. 2. **Convert mixed numbers to improper fractions:**

1. **Problem:** Given $a = -7i$ and $b = \frac{1}{6}i$, find $8(a + 2b)$. 2. **Formula and rules:** To solve this, use the distributive property and combine like terms. Remember th

1. **State the problem:** We need to add the fractions $\frac{1}{3}$ and $\frac{1}{4}$. 2. **Formula and rules:** To add fractions, they must have a common denominator. The formula

1. **State the problem:** Solve the equation $7(2k+1) = 3(4k-2)$ for $k$. 2. **Apply the distributive property:** Multiply out both sides:

1. The problem is to evaluate the expression $10|\sqrt{200}$, where $10$ is outside the square root and $\sqrt{200}$ is inside the root. 2. First, simplify the square root $\sqrt{2

1. Masalah: Tentukan asimtot dari fungsi yang diberikan. 2. Asimtot adalah garis yang mendekati grafik fungsi saat variabel mendekati nilai tertentu (biasanya tak hingga atau titik

1. **State the problem:** Solve the quadratic equation $$x^2 + x - 56 = 0$$. 2. **Recall the quadratic formula:** For an equation $$ax^2 + bx + c = 0$$, the solutions are given by

1. **State the problem:** Calculate the final price of a shirt originally priced at 80 with a 20% discount, then an additional 10% coupon discount on the sale price, and finally a

1. Diketahui fungsi $y = \log(x+1)$. Kita diminta menentukan domain fungsi, asimtotnya, dan grafik serta pergeseran dari grafik $y = \log x$. 2. Domain fungsi logaritma $y = \log(x

1. Let's start with Quadratic Equations and their roots and discriminant. A quadratic equation is of the form $$ax^2 + bx + c = 0$$ where $a \neq 0$.

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,