🧮 algebra

1. **Problem:** Solve the inequality $$x^4 + 35x^2 - 36 \geq 0$$. 2. **Formula and rules:** To solve polynomial inequalities, first find the roots by setting the expression equal t

1. **State the problem:** Solve the equation $$-12 = -2(2x - 5) - 22$$ for $x$. 2. **Use the distributive property:** Multiply $-2$ by each term inside the parentheses:

1. **State the problem:** Calculate the value of $$\sqrt[3]{81} + 8^{\frac{1}{3}}$$. 2. **Recall the cube root and exponent rules:** The cube root of a number $a$ is the same as $a

1. The problem asks to write an inequality for the situation where the number of days, $d$, of rain is not 17. 2. The key phrase here is "not 17," which means $d$ can be any number

1. The problem states: A minimum of 36 people, $p$, must ride in the bus. 2. To write an inequality for this situation, we need to express that the number of people $p$ is at least

1. The problem is to find points on the graph of the function $$f(x) = \frac{1}{2}x^2 + \frac{3}{5}x + 7$$ and understand how to calculate the corresponding $y$ values for given $x

1. **State the problem:** Solve for $x$ in the equation $7.19 = 6.1 + \log\left(\frac{6}{0.03x}\right)$. 2. **Isolate the logarithm:** Subtract 6.1 from both sides to get

1. **State the problem:** Solve for $x$ in the equation $7.19 = 6.1 + \log\left(\frac{6}{0.3x}\right)$. 2. **Isolate the logarithm:** Subtract 6.1 from both sides:

1. **Problem statement:** A quadratic polynomial $p(x)$ has $(2x + 1)$ as a factor. When $p(x)$ is divided by $(x - 1)$ and $(x - 2)$, the remainders are $-6$ and $-5$ respectively

1. **Problem statement:** A farmer has 24 meters of fencing to enclose a garden along the walls of an L-shaped house. The garden is divided into three equal sections for carrots, t

1. **State the problem:** Simplify the expression $$(5a - 9b - 2c) + (c + 7b + 3a)$$ by adding the opposite and gathering like terms. 2. **Recall the rule:** When adding expression

1. **Problem statement:** (i) Find the quadratic polynomial $p(x)$ given that $(2x+1)$ is a factor and the remainders when $p(x)$ is divided by $(x-1)$ and $(x-2)$ are $-6$ and $-5

1. **State the problem:** Simplify the algebraic expression by combining like terms: $$6x + 7a - 3x - 2a$$ 2. **Identify like terms:** Like terms have the same variable raised to t

1. The problem is to match each given function with its corresponding graph based on the description of the curves. 2. The functions are:

1. The problem is to match each given function with its corresponding graph based on the description of their shapes. 2. The functions are:

1. **State the problem:** We need to find the expression for the top base $B$ of a trapezoid given the area $A = 12x^2 - 29x + 14$, the bottom base $b = x - 5$, and the height $h =

1. **State the problem:** Calculate the value of the expression $$80 \div (|(-4)^3 + 10| - 14) + 12$$. 2. **Recall the order of operations:** Parentheses and absolute value first,

1. **State the problem:** Evaluate the expression $$12 + \left(\frac{2^5}{-8}\right) \times |12 - 15| + 5$$. 2. **Recall the order of operations:** Parentheses, Exponents, Multipli

1. **State the problem:** We are given the trapezoid area formula $$A = \frac{(B + b) \cdot h}{2}$$ and expressions for $$A$$, $$b$$, and $$h$$ in terms of $$x$$. We need to find t

1. **State the problem:** We have a piecewise function defined as: $$f(x) = \begin{cases} -x + 3, & x > 0 \\ 2x + 3, & x \leq 0 \end{cases}$$

1. **State the problem:** Solve the equation $$\frac{2x + 1}{4} + \frac{6x + 2}{5} = \frac{1}{4}$$ to find the value of $x$. 2. **Identify the formula and rules:** To solve equatio