🧮 algebra

1. **State the problem:** Solve the equation $$\frac{x}{14} + 222 = 8x$$ for $x$. 2. **Write down the formula and rules:** We want to isolate $x$ on one side. To do this, we will e

1. **State the problem:** We want to find the sum of all odd square numbers among the first 870,000 square numbers. 2. **Understanding odd squares:** Odd squares come from squaring

1. **State the problem:** We need to evaluate the function $$Q(y) = \frac{(y-4) + (y+4) - 5}{y-4}$$ at $$y=4$$. 2. **Write the function clearly:**

1. **State the problem:** Simplify the expression $2 \times 2 \times 2 \times 2 \times x$. 2. **Recall the rule:** Multiplying the same number repeatedly is expressed as an exponen

1. **State the problem:** Simplify the expression $$(2^x)^{-6} (8^x)$$. 2. **Recall the exponent rules:**

1. **State the problem:** Simplify the expression $$15. (2x)-6(8x)$$. 2. **Apply the distributive property:** Multiply the constants with the variables inside the parentheses.

1. **Problem:** Simplify the rational expression $$\frac{x^2+5x+6}{x^2-4} = N$$ 2. **Formula and rules:** Factor numerator and denominator.

1. **State the problem:** We need to calculate $\frac{1}{3}$ divided by $3$. 2. **Recall the division rule for fractions:** Dividing by a number is the same as multiplying by its r

1. **State the problem:** Simplify the expression $$4+\frac{1}{2}-(3-2)+3$$. 2. **Apply order of operations:** First, simplify inside the parentheses.

1. **State the problem:** Simplify the expression $$100-4\times5+\frac{60}{3}\times2-10+\frac{24}{6}\times3$$. 2. **Recall order of operations:** Perform multiplication and divisio

1. **State the problem:** Solve the inequality $$x^2 + 6x \geq -5$$. 2. **Rewrite the inequality:** Add 5 to both sides to get all terms on one side:

1. **State the problem:** Solve the inequality $$x^2 + 6x \geq -5$$. 2. **Rewrite the inequality:** Add 5 to both sides to get all terms on one side:

1. **Problem:** Model Romel's age 15 years ago. Let $r$ be Romel's current age.

1. **Problem Statement:** We need to redo the previous problem with all mathematical expressions wrapped in $...$ for inline math or $$...$$ for display math.

1. Problem: Use the given formulas to find unknown values by substitution and solving. ---

1. Consider the rule $$R = 5b - 3$$. (a) Find $$R$$ if $$b = 2$$:

1. **Stating the problem:** We want to understand the relationship between the time taken to pass in the opposite direction and the time taken to pass in the same direction, given

1. **Problem Statement:** We are given two trains with speeds $v_1$ and $v_2$ where $v_1 > v_2$. The ratio of their speeds is equal to the ratio of the time taken to pass each othe

1. **State the problem:** We need to complete the table for $f(x) = \frac{1}{2}|x|$ and $g(x) = 2^x$ at $x = -1, 0, 1$ and determine where $f(x) = g(x)$. 2. **Calculate $f(x)$ valu

1. **State the problem:** We need to complete the table for $f(x) = |x - 3| - 4$ and $g(x) = 3^x - 5$ at $x = 1, 3, 4$ and determine where $f(x) = g(x)$ has a solution. 2. **Calcul

1. **State the problem:** We need to complete the table for $f(x) = \frac{1}{3} x + 2$ and $g(x) = 2^{x + 3}$ at $x = -3, -2, 0$ and then determine where $f(x) = g(x)$ has a soluti