🧮 algebra

1. **State the problem:** Solve the equation $h - 7\left(\frac{5}{6}\right) = 5\left(\frac{1}{2}\right)$ for $h$. 2. **Write down the equation:**

1. The problem asks to find the values of $x, y, z$ such that the numbers $x^2 - yz$, $y^2 - xz$, and $z^2 - xy$ form an arithmetic progression (AP) of 4 terms. 2. Recall that for

1. **State the problem:** Solve the system of inequalities by graphing: $$y \leq 3x + 3$$

1. Let's factor the quadratic expression $x^2 + 5x + 6$. 2. The problem is to express $x^2 + 5x + 6$ as a product of two binomials.

1. **State the problem:** We need to find the equation of the trend line passing through the points (2, 1) and (6, 8) in slope-intercept form $y=mx+b$. 2. **Formula for slope:** Th

1. **Problem Statement:** Simplify the algebraic expression $7a^2 - 11a + 24 - a - 7a + 2(a^2 - 2a + 3) - 3(-a^2 - 3a - 4) + 2(2a^2 - 7a + 6) + 5a^2 - a + 18 - 3(a^2 + 4 - a)$. 2.

1. **State the problem:** We need to find the equation of the trend line passing through the two yellow points on the scatter plot, which are approximately at coordinates $(1, 2)$

1. The problem asks why $a^2 + b^2$ is different from $(a + b)^2$. 2. The formula for the square of a sum is:

1. **State the problem:** We need to find the equation of the trend line passing through the two blue points on the scatter plot, which are approximately at coordinates $(3,9)$ and

1. **Problem statement:** Factor the expression given (assuming a general expression since none was specified). 2. **Formula and rules:** To factor an algebraic expression, look fo

1. The problem is to solve a math question suitable for grade 7 level. Since no specific problem was given, let's consider a common grade 7 algebra problem: Solve for $x$ in the eq

1. The problem asks what happens to the function $L(X)$ when $X$ takes values in the set $\{0.1, 0.01, 0.001, 0.0001, 0.00001\}$. 2. To analyze this, we first need to know the expl

1. The problem asks why the least common denominator (LCD) is $6(x+1)$. 2. The LCD is the smallest expression that all denominators in a set of fractions can divide into without le

1. **State the problem:** Solve the equation $$\frac{3}{x+1} - \frac{1}{2} = \frac{1}{3x+3}$$. 2. **Rewrite the equation:** Notice that $$3x+3 = 3(x+1)$$, so the equation becomes:

1. **State the problem:** Solve for $x$ in the equation $$\left(\frac{1}{8}\right)^x = 25.$$\n\n2. **Recall the formula and rules:** When solving exponential equations, we often ta

1. **State the problem:** Solve for $x$ in the equation $$5^{-3x} - 1 = 25.$$\n\n2. **Rewrite the equation:** Add 1 to both sides to isolate the exponential term:\n$$5^{-3x} = 26.$

1. **State the problem:** Solve for $x$ in the equation $5 - 3x - 1 = 25$. 2. **Simplify the equation:** Combine like terms on the left side:

1. **State the problem:** Solve the equation $$\frac{1}{x} = \frac{4}{3x} + 1$$ for $x$. 2. **Identify the formula and rules:** We want to isolate $x$. Since the equation involves

1. The problem asks: What percentage is 3 of 12? 2. To find what percentage one number is of another, use the formula:

1. The problem is to understand and simplify the expression $A=\binom{n}{k}\frac{a}{b}$. 2. The binomial coefficient $\binom{n}{k}$ represents the number of ways to choose $k$ elem

1. The problem states that the given relation is a function, and we want to add one ordered pair to it so that the new relation remains a function. 2. A function assigns exactly on