🧮 algebra

1. Consider the expression: $$3(x - 2) - 4(x + 5)$$. 2. The problem is to simplify this expression by removing the brackets and combining like terms.

1. **State the problem:** We have the quadratic equation $x^2 - (m - 1)x + m + 2 = 0$ and want to find the values of $m$ for different root conditions. 2. **Recall discriminant for

1. Let's start by understanding what the absolute value means. 2. The absolute value of a number is the distance that number is from zero on the number line, regardless of directio

1. Masalah: Diberikan barisan geometri dengan suku pertama $a_1=3,6\sqrt{2}$ dan suku-suku berikutnya $24, 48/2, ..., 98.304$. Diketahui banyaknya suku barisan tersebut adalah ganj

1. Misalkan suku pertama barisan geometri adalah $a$ dan rasio adalah $r$. 2. Suku ketiga adalah $a r^2$, dan diketahui $a r^2 = a + 6$.

1. Diberikan fungsi kubik taman kota: $$y = x^3 - 4x$$. Kita ingin menentukan luas total daerah antara grafik fungsi dan sumbu x dari $$x = -2$$ sampai $$x = 0$$. 2. Karena fungsi

1. The problem asks to evaluate the absolute values of the given numbers: -3, 0, 3, and to evaluate |−100| and |100|. 2. Recall that the absolute value of a number $x$, denoted $|x

1. Problem: Evaluate the absolute value function $|x|$ at $x=-3,0,3,100,-100$ and explain the piecewise definition and graph. 2. Recall the definition of absolute value.

1. Masalah yang diberikan melibatkan fungsi kubik $$y = x^3 - 4x$$ yang menggambarkan taman yang terbagi menjadi tiga daerah oleh kurva tersebut. 2. Pertama, kita cari titik potong

1. **State the problem:** We need to evaluate the limit $$\lim_{x \to -2} \frac{x^{2} + 4x + 4}{x^{2} - 2x - 8}$$. 2. **Factor numerator and denominator:**

1. Problem: Simplify the expression $\dfrac{125m x^{-4}}{\dfrac{x^2 \cdot x \cdot \sqrt{x^4}}{25}}$. 2. Note that $\sqrt{x^4}=x^2$ for $x\ge 0$.

1. Let's start by stating what logarithmic equations are: equations that involve the logarithm of a variable. 2. A common form is $\log_a(x) = b$, which means $x = a^b$.

1. Algebra is a branch of mathematics dealing with symbols and the rules for manipulating these symbols. 2. The fundamental concept is to solve equations where variables represent

1. **Simplify** the expression $$\sqrt[3]{\frac{125 \times x^{-4}}{x^2}} \times \sqrt{\frac{x^4}{25}}$$. 2. Apply laws of exponents inside the cube root:

1. **State the problem:** Solve the equation $$ \sqrt{27g + 513} = 3g + 3 $$ to find the value(s) of $g$. 2. **Isolate and square both sides:** To eliminate the square root, square

1. Solve $17x + 12 = 54 - 4x$. Add $4x$ and subtract $12$: $$17x + 4x = 54 - 12$$

1. **State the problem:** Solve the equation $$\sqrt{8f + 5} = \sqrt{4f + 8}$$. 2. **Square both sides** to eliminate the square roots: $$\left(\sqrt{8f + 5}\right)^2 = \left(\sqrt

1. **State the problem:** Solve the equation $$\sqrt{6w + 5} = \sqrt{2w + 8}$$. 2. **Square both sides** to eliminate the square roots:

1. The problem is to solve the equation $3\sqrt[n]{x}w + 1 = 1$ for $x$. 2. Start by subtracting 1 from both sides to isolate the term with $x$:

1. Stating the problem: We need to solve for $j$ in the equation $$\sqrt[3]{4j + 4} = 5$$. 2. To eliminate the cube root, cube both sides of the equation:

1. **State the Problem:** Given the line equation $$6y - 8x - 10 = 0$$, find: I. The slope and intercept of line L₁.