🧮 algebra

1. **State the problem:** Simplify the expression $4(-x-16)$. 2. **Formula and rules:** Use the distributive property which states $a(b+c) = ab + ac$.

1. **State the problem:** Simplify the expression $3(-9x - 6y)$. 2. **Formula and rules:** Use the distributive property which states $a(b + c) = ab + ac$. Here, $a=3$, $b=-9x$, an

1. **State the problem:** Solve the equation $3x + 10 = 2x - 5m$ for $x$. 2. **Isolate the variable $x$:** To solve for $x$, we want to get all terms containing $x$ on one side and

1. **Problem:** One root of the quadratic equation $x^2 - (k^2 - 4k + 4)x + 9 = 0$ is the additive inverse of the other. Find $k$. 2. **Formula and rules:** For a quadratic equatio

1. **State the problem:** Simplify the expression $11(-5-3m)$. 2. **Formula and rules:** Use the distributive property: $a(b+c) = ab + ac$.

1. **State the problem:** Simplify the expression $5(y+4)$. 2. **Formula used:** Use the distributive property of multiplication over addition:

1. **State the problem:** Simplify the expression $3(x-9)$. 2. **Formula used:** Use the distributive property $a(b+c) = ab + ac$.

1. The problem states that we divided a number and received 378,000 as the result. 2. To find the original number, we need to know what number we divided by. Since the divisor is n

1. The problem is to simplify the expression $6a + a^{\frac{1}{2}} b^{\frac{1}{3}} - 15 b^{\frac{2}{3}}$. 2. This expression contains terms with variables $a$ and $b$ raised to fra

1. The problem is to find the unit prices for each item in the table by dividing the total price by the quantity, then sum all unit prices to verify the total price $379,673.01$. 2

1. **Problem statement:** Simplify the expression $(-5q^2 + 3p - 2q + p^2) + (4p + q + pq)$. 2. **Formula and rules:** To simplify, combine like terms. Like terms have the same var

1. **State the problem:** Simplify the expression $ (6 - 7x + x^2) + (6x - 6x^2 + 10) $. 2. **Write down the expression:**

1. **Problem 1a: Analyze the equation $|y| = x$.** - The equation states that the absolute value of $y$ equals $x$.

1. **State the problem:** Simplify the expression $$(-7p - 3) + (p^2 + 5)$$. 2. **Recall the rules:** When adding algebraic expressions, combine like terms. Like terms have the sam

1. **State the problem:** We need to find the linear equation in slope-intercept form $y = mx + b$ that fits the given table of points: $(4, 28)$, $(5, 29)$, $(6, 30)$, and $(7, 31

1. **State the problem:** Evaluate $$\left[ \left(-\frac{4}{11}\right)^{\frac{4}{5}} \cdot \left(-\frac{4}{11}\right)^{-\frac{4}{5}} \right]^7$$. 2. **Recall the exponent rule:** W

1. **State the problem:** Evaluate the expression $$\left[\left(-\frac{4}{11}\right)^{\frac{4}{5}} \cdot \left(-\frac{4}{11}\right)^{-\frac{4}{5}}\right].$$ 2. **Recall the exponen

1. The problem asks to find the 20th term of the sequence defined by $T_n = 3^n$. 2. The formula for the $n^{th}$ term of this sequence is $T_n = 3^n$, which means each term is 3 r

1. **State the problem:** Solve the equation $x - 3 = 5x + 7$ and check the solution. 2. **Write the equation:**

1. **State the problem:** We need to evaluate each expression and then organize the results from least to greatest. 2. **Evaluate each expression:**

1. The problem asks us to show that the sequence $1, -1, 1, -1, 1, -1, \ldots$ defined by the general term $a_n = (-1)^{n+1}$ diverges. 2. Recall that a sequence converges if it ap