🧮 algebra

1. **State the problem:** Solve the equation $X - \frac{1}{2} + 3X = 10$ for $X$. 2. **Combine like terms:** The terms with $X$ are $X$ and $3X$, so add them:

1. **State the problem:** Simplify the expression $$(a - 3b) 5a + (2b + 3b + 5b)$$. 2. **Apply distributive property:** Multiply $5a$ by each term inside the first parentheses:

1. **State the problem:** We need to simplify the expression $$\frac{3}{4} + \frac{1}{2} \div 5$$. 2. **Recall the order of operations:** Division and multiplication are performed

1. **State the problem:** Solve the equation $|2x + 3| = 9$. 2. **Recall the definition of absolute value:** For any expression $A$, $|A| = B$ means $A = B$ or $A = -B$ when $B \ge

1. **Problem ①:** Simplify the expression $$-6 - (-3 + 7) + 10$$. 2. **Step 1:** Evaluate inside the parentheses first: $$-3 + 7 = 4$$.

1. **Stating the problem:** Find the least common multiple (LCM) of the numbers given by their prime factorizations: - $2^2 \times 3$

1. **State the problem:** Solve the equation $3(x+5) + 4(x+5) = 25$ for $x$. 2. **Use the distributive property:** Multiply each term inside the parentheses by the coefficients.

1. **Stating the problem:** Empat petugas dapat mengetik enam dokumen dalam waktu tujuh hari. Berapa lama waktu yang dibutuhkan tujuh petugas untuk mengetik 12 dokumen jika kecepat

1. **State the problem:** We are given the system of equations:

1. **Problem Statement:** Solve the system of linear equations using Gaussian elimination: $$\begin{cases} w - x + 3y - 3z = 3 \\ -5w + 2x - 5y + 4z = -5 \\ -3w - 4x + 7y + 2z = 7

1. **Problem 3:** Solve $$\frac{(x - 3)(x + 5)(x - 7)}{|x - 4|(x + 6)} \leq 0$$ 2. **Step 1:** Identify critical points where numerator or denominator is zero or undefined:

1. **Problem 1: For the function $f(x) = 2x + 5$** a) The domain of $f(x)$ is all real numbers because it is a linear function with no restrictions. So, domain: $(-\infty, \infty)$

1. **State the problem:** Solve the system of linear equations: $$\begin{cases} w - x + 3y - 3z = 3 \\ -5w + 2x - 5y + 4z = -5 \\ -3w - 4x + 7y + 2z = 7 \\ 2w + 3x + y - 11z = 1 \e

1. Solve $\frac{x(3 - 4x)(x + 1)}{2x - 5} < 0$. - Factor and find critical points: $x=0$, $x=\frac{3}{4}$, $x=-1$, $x=\frac{5}{2}$ (denominator zero).

1. **State the problem:** Calculate the value of $$(1.874)^{\frac{1}{5}} - 1$$. 2. **Recall the formula:** The expression involves the fifth root of 1.874, which can be written as

1. **State the problem:** Solve the system of equations: $$x^2 + y^2 + z^2 = 14$$

1. The problem asks us to predict the cost of the electricity bill after 15 days using the trend line equation. 2. The given trend line equation is $$y = 3x + 5$$ where $x$ is the

1. **State the problem:** Solve the quadratic equation $$x^2 + 5x = 12$$ and give solutions correct to 3 significant figures. 2. **Rewrite the equation in standard form:** Move all

1. **State the problem:** We need to find the equation of a line perpendicular to the line given by $$y = -\frac{1}{2}x - 1$$ that passes through the point $(-2, 4)$. The answer sh

1. **State the problem:** Find the equation of the line perpendicular to $y = \frac{1}{2}x - 9$ that passes through the point $(3, 2)$. 2. **Recall the formula:** The point-slope f

1. **State the problem:** Find the equation of the line perpendicular to $$y = -\frac{1}{8}x + 4$$ that passes through the point $$(2, 3)$$ in point-slope form. 2. **Recall the poi