🧮 algebra

1. **State the problem:** Seven less than a number divided by 3 is five. 2. **Define the variable:** Let the number be $x$.

1. **State the problem:** We need to analyze and graph the rational function $$R(x) = \frac{7}{x^2 - 16}$$ including its domain, intercepts, and simplification. 2. **Find the domai

1. **State the problem:** We need to analyze and graph the rational function $$R(x) = \frac{7}{x^2 - 16}$$ and find its domain. 2. **Factor the denominator:** The denominator is a

1. **Problem:** Solve the equation $$\frac{2}{3}x + \frac{3}{8} = \frac{3}{4}$$ for $$x$$. 2. **Formula and rules:** To solve for $$x$$, isolate $$x$$ by subtracting and dividing.

1. **State the problem:** Simplify the expression $2[ -65 - 43(75 - 98)]$. 2. **Apply the order of operations:** Start by simplifying inside the parentheses.

1. **State the problem:** Simplify the expression $3[87 - 32(94 - 65)]$. 2. **Recall the order of operations:** Parentheses first, then multiplication, then addition/subtraction.

1. The problem asks to identify the location of points on the coordinate plane and determine their quadrant or axis. 2. Recall the rules for quadrants:

1. **Problem Statement:** You want to understand how to evaluate and simplify algebraic expressions step-by-step. 2. **Substitution:** When you have an expression like $2y + 3$ and

1. **Problem Statement:** We are given algebraic expressions and values for variables, and we want to evaluate these expressions step-by-step. 2. **Evaluating an expression:** When

1. State the problem: Solve the equation $$2x + 3 = 7$$. 2. Use the formula for solving linear equations: isolate the variable by performing inverse operations.

1. The problem asks if you need to find the cubic root of the other side of the equation when solving for a variable that is cubed. 2. When you have an equation like $x^3 = a$, to

1. **State the problem:** We are given the area of a rectangular pool deck as $3x^2 + 11x - 20$ square meters and the width as $x + 5$ meters. We need to find the length. 2. **Form

1. **State the problem:** Calculate the value of $-22 - (-58)$. 2. **Recall the rule:** Subtracting a negative number is the same as adding its positive counterpart. So, $a - (-b)

1. **State the problem:** Solve the equation $x + 46 = 73$ for $x$. 2. **Formula and rules:** To isolate $x$, subtract 46 from both sides of the equation. This uses the subtraction

1. Resolver as potências: **a)** $(\frac{1}{6})^2 = \frac{1^2}{6^2} = \frac{1}{36}$

1. **State the problem:** Jhia runs 100 m four times each training day. Last week she trained 4 days, this week 5 days. We need to find the total metres she ran in the last 2 weeks

1. Problem: Multiply the monomial by the polynomial for the first expression: $a(4a + 3)$. 2. Formula: Use the distributive property $a(b + c) = ab + ac$ to multiply each term insi

1. **State the problem:** We have four stacks of cubes with heights 5, 4, 7, and 8 cubes respectively. 2. **Goal:** Rearrange the cubes so that each of the four stacks has an equal

1. **State the problem:** Simplify and express with positive exponents the following expressions: a) $$\left( \frac{a^{-2}}{b^{-5}} \right)^{-3}$$

1. Planteamos el problema: Resolver la inequación $$\frac{x-2}{x} \leq 0$$. 2. Recordemos que una fracción es menor o igual a cero cuando el numerador y denominador tienen signos o

1. **State the problem:** Simplify the expression $$\left(\frac{12x^3y^{-1}}{-8x^{-1}y^5}\right)^{-2}$$ and express the result with positive exponents. 2. **Recall the rules:**