🧮 algebra

1. The problem asks which of the given equations have a solution of 7. 2. To determine if 7 is a solution, substitute $x=7$ into each equation and check if the equation holds true.

1. **State the problem:** We need to determine which ordered pairs satisfy the linear equation $$y = 6x + 4$$ exactly. 2. **Recall the formula:** For each ordered pair $ (x, y) $,

1. The problem is to match each given equation with the correct graph description, knowing the green graph is always $y=x^2$. 2. Recall the forms and effects of transformations on

1. **State the problem:** Solve the equation $3(2x+5)=39$ for $x$. 2. **Use the distributive property:** Multiply 3 by each term inside the parentheses.

1. **State the problem:** Solve the system of linear equations: $$x + y = 3$$

1. **State the problem:** We need to graph the piecewise function:

1. **Stating the problem:** We are given a piecewise function $f(x)$ defined by two segments: - A horizontal line segment from $(-3, -4)$ to $(0, -4)$ with filled endpoints.

1. **Problem:** Find the least common denominator (LCD) for the expression $$\frac{3}{x+4} + \frac{x}{x^2 - 16} + \frac{x+2}{4}$$ 2. **Step 1: Factor all denominators.**

1. **State the problem:** We need to find the value of $x$ such that $f(x) = g(x)$, where $f(x) = 2 + 3x$ and $g(x) = 7x + 1$. 2. **Set the functions equal:** Since $f(x) = g(x)$,

1. Let's clarify the problem: You are asking why in the linear equation $y = mx + b$, the $b$ value is not just a constant but sometimes appears to multiply $x$ or be reversed in m

1. The problem asks to find the original points A and B before the transformations given the transformed points A' and B'. 2. The transformations applied are:

1. **Problem Statement:** We analyze a graph of a downward-opening parabola starting near $x=0$, peaking near $x=2$, and falling by $x=4$.

1. **State the problem:** We need to find the linear equation relating price $x$ to sales $y$ given two points $(6, 3000)$ and $(8, 2000)$, then use it to predict sales at price $6

1. **State the problem:** You have a mixture ratio of water to release agent as 8:1. You are using 32 ounces of water and want to find how many ounces of release agent to mix. 2. *

1. **State the problem:** We need to write an equation in slope-intercept form $y = mx + b$ that represents the monthly cost $y$ of the farm when it produces $x$ eggs.

1. **State the problem:** Solve the first equation given: $$50x \cdot 7 + 3 = 3x - \frac{5x}{4}$$ 2. **Rewrite the equation:** Multiply and simplify terms:

1. The problem is to solve the inequality $X - y < 2$ for $y$. 2. Start with the inequality:

1. **State the problem:** Find the equation of the line parallel to $y = -6x + 3$ that passes through the point $(-2, 16)$. 2. **Recall the rule for parallel lines:** Parallel line

1. **State the problem:** Simplify the expression $$\left(\frac{2x^{-3} y^{-2}}{3x^{-2} y^3}\right)^{-2}$$ and then evaluate it for $x = -2$ and $y = 3$. 2. **Use the laws of expon

1. The problem asks to find the best approximate solutions of the system of equations where $f(x)$ and $g(x)$ intersect. 2. The intersection points occur where $f(x) = g(x)$.

1. **State the problem:** Find the equation of the line parallel to $y=3x-2$ that passes through the point $(2,11)$. 2. **Recall the rule for parallel lines:** Parallel lines have