🧮 algebra

1. **State the problem:** Solve the equation $$\frac{2x - 5}{6} - \frac{3x - 4}{8} = 0$$. 2. **Formula and rules:** To solve equations involving fractions, find a common denominato

1. **Stating the problem:** For problem 9, we have a fraction $\frac{3}{4}$ on the left and the number 20 on the right of a U-shaped graph with a square box inside near the right s

1. **State the problem:** We need to solve the equation $$\frac{2x+4}{x-3} = 3$$ for $x$. 2. **Recall the formula and rules:** To solve a rational equation like this, multiply both

1. **State the problem:** We need to find the value of $x$ in the proportion $\frac{15}{66} = \frac{x}{99}$.\n\n2. **Use the cross-multiplication formula:** For two ratios $\frac{a

1. **State the problem:** We need to find a cubic polynomial $p(x) = ax^3 + bx^2 + cx + d$ such that it passes through the points $(1,24)$, $(3,120)$, $(5,336)$, and $(7,720)$. The

1. **State the problem:** We need to find the pounds of chocolate eaten per capita in the U.S. given the total population and total chocolate consumption. 2. **Given data:**

1. The problem is to find the least common multiple (LCM) of given denominators. 2. The LCM of denominators is the smallest number that each denominator divides into without leavin

1. **State the problem:** Find the least common multiple (LCM) of the fractions $\frac{3}{7}$, $\frac{5}{5}$, and $\frac{1}{6}$.\n\n2. **Recall the formula for LCM of fractions:**

1. **State the problem:** Solve for $c$ in the equation $$\frac{1}{4}(1+3c) + \frac{1}{4}(1-c) + \frac{1}{4}(1+2c) + \frac{1}{4}(1-4c) = 1.$$\n\n2. **Write the equation clearly:**\

1. **State the problem:** We want to find out how much money each person would get if a jackpot of 7.3 billion dollars is divided equally among 320 million people. 2. **Formula use

1. The problem states: The parabola $y = 3(x - 4)(x + 2)$ has $x$-intercepts at $(-4, 0)$ and $(2, 0)$. We need to verify if this is true or false. 2. Recall that $x$-intercepts oc

1. **State the problem:** Simplify the expression $2\frac{a}{b}5 - \sqrt{x}5$. 2. **Rewrite the expression:** The term $2\frac{a}{b}5$ means $2 \times \frac{a}{b} \times 5$.

1. El problema es simplificar la expresión o resolver la ecuación dada sin explicaciones extensas. 2. Usamos las reglas básicas de álgebra: sumar, restar, multiplicar, dividir y si

1. **State the problem:** We are given the quadratic function $y = x^2 + 2x - 3$ and want to analyze it. 2. **Formula and rules:** The general form of a quadratic function is $y =

1. **State the problem:** Solve the equation $2^x = 7 + 2^{2-x}$ for $x$. 2. **Rewrite the equation:** The equation is $2^x = 7 + 2^{2-x}$.

1. **Problem Statement:** Find the volume $V$ when $V = \frac{1}{3}Ah$, $A = 43$, and $h = 6$. 2. **Formula:** The volume of a pyramid or cone is given by

1. **Problem Statement:** We are asked to complete the table of values for the function $$y = 2x^2 - 7x - 3$$ for $$x = -2, -1, 0, 1, 2, 3, 4, 5$$.

1. Stating the problem: Simplify the expression $-3[2 - (5 - 4) + (-6)] + 7 - (-2 \cdot 3)$. 2. Simplify inside the parentheses: Calculate $(5 - 4) = 1$.

1. **State the problem:** We need to find how many 64ths are in $\frac{3}{16}$. This means we want to express $\frac{3}{16}$ as a number of parts each of size $\frac{1}{64}$. 2. **

1. **State the problem:** Emman had $\frac{3}{4}$ of a box of chocolates. He gave $\frac{2}{3}$ of his chocolates to Lizette. Then Lizette gave $\frac{1}{2}$ of her chocolates to A

1. **State the problem:** We have a table of values for $x$ and $y$: | $x$ | 1 | 2 | 3 | 4 | 5 |