🧮 algebra

1. **State the problem:** Solve the linear equation $4x + 2 = -6$ for $x$. 2. **Formula and rules:** To solve for $x$, isolate $x$ by performing inverse operations. Remember, whate

1. The problem is to write an equation for a line. 2. The general form of a line equation is $$y = mx + b$$ where $m$ is the slope and $b$ is the y-intercept.

1. **State the problem:** We are given a point $(-3,6)$ on a line with slope $4$, and we need to find two more points on this line. 2. **Recall the formula:** The slope formula is

1. **State the problem:** Solve the equation $a + b + 20 = 60$ for $a + b$. 2. **Identify the goal:** We want to find the value of $a + b$.

1. **State the problem:** Simplify the expression $$\left(\frac{x}{7}\right)^2$$. 2. **Recall the formula:** When you square a fraction, you square both the numerator and the denom

1. **State the problem:** Simplify the expression $$\left(\frac{x}{3}\right)^3$$. 2. **Recall the power of a quotient rule:** $\left(\frac{a}{b}\right)^n = \frac{a^n}{b^n}$.

1. **State the problem:** Calculate the sum of $-7$ and $-5$. 2. **Recall the rule for adding negative numbers:** When adding two negative numbers, add their absolute values and ke

1. The problem is about adding and subtracting integers in word problems. 2. When adding integers, if both numbers have the same sign, add their absolute values and keep the sign.

1. **State the problem:** We need to find the piecewise function $f(x)$ defined on two intervals: $[-1,1]$ and $[3,5]$ based on the given points. 2. **Analyze the first segment:**

1. **State the problem:** We have a piecewise function defined as: $$

1. **Problem Statement:** We are given the function $$f(x) = \frac{3x+5}{x^2+3x+2}$$ defined on the interval $$0 \leq x \leq 1$$.

1. **State the problem:** Simplify the expression $$(x-4)^2$$. 2. **Recall the formula:** The square of a binomial is given by $$ (a-b)^2 = a^2 - 2ab + b^2 $$.

1. **State the problem:** We need to expand and simplify the expression $$(x+5)(x+6)$$. 2. **Formula used:** To expand two binomials, we use the distributive property (also known a

1. **State the problem:** We know the average of 5 numbers is $82$, and three of these numbers are $53$, $65$, and $72$. We need to find the average of the other 2 numbers. 2. **Re

1. The problem is to subtract the complex numbers $(9 + 4i)$ and $(2 + 2i)$. 2. The formula for subtracting complex numbers is:

1. **State the problem:** Multiply the complex numbers $5 + 7i$ and $8 - 2i$. 2. **Recall the formula:** To multiply two complex numbers $(a + bi)(c + di)$, use the distributive pr

1. **State the problem:** We want to estimate the value of $$\frac{13.7 + 1.28}{5.099}$$ by rounding each number to the same number of significant figures and then calculating the

1. **State the problem:** We need to find how many pounds of aluminum cans Severo recycled if he received 906¢ and the average price was 75 1/2¢ per pound. 2. **Convert mixed numbe

1. **State the problem:** We need to find the average rainfall per hour given that 10 6/7 inches of rain fell over 24 hours. 2. **Convert the mixed number to an improper fraction:*

1. **State the problem:** Adi drives from home to her office in 2 hours at a certain speed. If she drives 15 mph slower, it takes her 3 hours. We need to find the distance between

1. **State the problem:** We need to find the dilation factor of the function $$y=-(x+2)^3$$. 2. **Recall the dilation concept:** A dilation factor in a function typically refers t