🧮 algebra

1. **State the problem:** Solve the inequality $ (3 - x)(5x + 8) \geq 9 - 3x $. 2. **Expand the left side:** Use distributive property:

1. **State the problem:** We need to find an expression for "a certain number decreased by 5 twice the number." Let the certain number be $x$. 2. **Translate the problem into an al

1. **Stating the problem:** Solve the system of linear equations for $x_3$: $$\begin{cases} 2x_1 - x_2 - x_3 = 4 \\ 3x_1 + 4x_2 - 2x_3 = 11 \\ 3x_1 - 2x_2 + 4x_3 = 11 \end{cases}$$

1. **State the problem:** Solve the system of equations graphically: $$y = \frac{5}{2}x - 8$$

1. **State the problem:** Solve the system of equations by substitution: $$y = 6x$$

1. Let's start by understanding your request: you want a clear, step-by-step explanation similar to how teachers write in notebooks. 2. Since you did not specify a particular math

1. **Problem Statement:** Determine the inequality represented by the graph with a red line passing through points near $(0,5)$ and $(2.5,0)$, and the shaded region to the right of

1. **State the problem:** We need to evaluate the expression $$8p + 3q - 18$$ when $$p = \frac{1}{2}$$ and $$q = 7$$. 2. **Write the expression:** $$8p + 3q - 18$$.

1. The problem asks: What two numbers add up to 56? 2. The formula for addition is $a + b = 56$, where $a$ and $b$ are the two numbers.

1. The problem states that Tlaloc pumped up 56 balls in total, with a ratio of 5 dodge balls for every 9 other balls. 2. The original ratio is dodge balls : other balls = 5 : 9.

1. The problem states that the expression $$62.4d - 210$$ gives the number of Indian rupees you receive when you exchange $$d$$ dollars. 2. We are asked to find how many Indian rup

1. The problem asks to find three ratios equivalent to 5 : 2. 2. Two ratios are equivalent if their fractions are equal. That means \( \frac{a}{b} = \frac{c}{d} \).

1. The problem states the sequence $x_n = cn + d$, where $c$ and $d$ are constants. 2. This is an arithmetic sequence, where each term increases by a constant difference $c$.

1. **State the problem:** We are given the function $$y = -\frac{1}{x+2}$$ and a set of points plotted on its graph. We need to verify if the point at $x=1$ is correct. 2. **Recall

1. **State the problem:** Solve the system of equations using the elimination method: $$6x + 3y + 4 = 0$$

1. The problem asks to verify if the expression $4 \times 4 - 5 \times 3$ equals 1. 2. Calculate the value:

1. **State the problem:** Calculate the value of the expression $$2^4 \times \frac{1}{(-2)^3}$$. 2. **Recall the rules:**

1. Énonçons le problème : Résoudre l'équation $$2x + (1 - \sqrt{2})x - y = 0$$. 2. Regroupons les termes en $x$ : $$2x + (1 - \sqrt{2})x = \bigl(2 + 1 - \sqrt{2}\bigr)x = (3 - \sqr

1. **State the problem:** We are given two linear functions: $$y=\frac{1}{4}x+6$$

1. **State the problem:** Find the point of intersection of the two lines given by the equations: $$y = x + 7$$

1. We are asked to find the equation of the red straight line passing approximately through points (-3,-3) and (3,5). 2. The formula for the equation of a line given two points $(x