🧮 algebra

1. **Problem statement:** Determine the slope of each line given the descriptions. 2. **Recall the slope formula:** For two points $(x_1,y_1)$ and $(x_2,y_2)$, the slope $m$ is giv

1. **State the problem:** Juno starts with 150 in their bank account and spends 10 each week. We want to find how many weeks it takes for Juno to have 520 in the account. 2. **Anal

1. **Problem statement:** Given points $A(2,3)$ and $B(-1,-4)$, find the distance $|AB|$. 2. **Formula for distance between two points:**

1. The problem is to simplify the expression $-\left|-x\right|$. 2. Recall that the absolute value function $|a|$ returns the non-negative value of $a$, so $|-x| = |x|$ because abs

1. **Problem:** Simplify the expression $2a^2b + 3ab - a^2b + 2ab$. 2. **Step 1:** Group like terms. Terms with $a^2b$ are $2a^2b$ and $-a^2b$. Terms with $ab$ are $3ab$ and $2ab$.

1. **State the problem:** Find the solution or roots of the quadratic function $f(x) = x^2 - 3x - 7$. 2. **Formula used:** To find the roots of a quadratic equation $ax^2 + bx + c

1. The problem is to understand why $\frac{8}{5} \div 3$ equals $\frac{8}{15}$.\n\n2. When dividing fractions or numbers, remember the rule: dividing by a number is the same as mul

1. **State the problem:** We are given the sum of the first $n$ terms of a sequence as $S_n = n^2 + 3n$. We need to find the terms of the sequence and check if it forms an arithmet

1. **State the problem:** We are given the sum of the first $n$ terms of a sequence as $S_n = n^2 + 3n$. We need to find the terms of the sequence and check if it forms an arithmet

1. The problem is to write an expression or equation all together in steps without dividing it into separate parts. 2. To do this, we first identify the full expression or equation

1. **State the problem:** We need to find the graphical representation of the two lines given by the equations: $$-8x + 6y = -22$$

1. **State the problem:** Find the x-intercept and y-intercept of the line given by the equation $$y + 1 = 3(x - 4)$$. 2. **Rewrite the equation in slope-intercept form:**

1. The problem is to understand if the power 2 in $x^2=0$ can be removed. 2. The equation given is $x^2=0$.

1. **State the problem:** We need to determine which graph represents the inequality $$2x + 3y \leq 6$$. 2. **Rewrite the inequality in slope-intercept form:**

1. **State the problem:** Simplify the complex fraction $$\frac{\frac{x}{81} + \frac{1}{x}}{\frac{5}{81} - \frac{5}{9x}}$$. 2. **Rewrite the numerator and denominator:**

1. The problem is to solve the equation $$|x - 1| = 5$$ where the expression inside the absolute value is $x - 1$. 2. Recall that the absolute value equation $|A| = B$ means $A = B

1. **State the problem:** Simplify the expression $$\frac{3 + \frac{7}{6x}}{1 - \frac{1}{12x}}$$. 2. **Rewrite the expression:** To simplify, first write the numerator and denomina

1. **Stating the problem:** Solve the simultaneous equations for variables $x$ and $y$. 2. **General approach:** To solve simultaneous equations, we use substitution or elimination

1. The problem is to solve the equation $$| |x| | = 5$$. 2. The absolute value function $|x|$ returns the non-negative value of $x$. Applying absolute value twice, as in $| |x| |$,

1. The problem is to understand and simplify expressions involving double absolute values, such as $| |x| |$. 2. The absolute value function $|x|$ returns the non-negative value of

1. The problem is to understand when to use infinities in solving absolute value equations. 2. Absolute value equations have the form $|x| = a$, where $a \geq 0$.