🧮 algebra

1. **State the problem:** Find the value of $p$ such that the expressions $2(p + 5)$ and $3(2p - 1)$ are equal. 2. **Write the equation:**

1. **State the problem:** We are given a table showing the labour hours, wood blocks, and paint tins required to manufacture toy buses and trains, along with their costs. We need t

1. **Problem:** Office Products has a box of 250 binder clips on sale for 9.99. The list price is 10.99. If you buy 4 boxes, find (a) sale price, (b) amount you save, and (c) total

1. **State the problem:** We are given a rectangle where the length $l$ is 4 units greater than the width $w$, so $l = w + 4$. The perimeter $P$ of the rectangle is given by the fo

1. **State the problem:** We are given the perimeter formula for a rectangle: $$P = 2(x + y)$$ where $x$ and $y$ are the lengths of the sides. 2. **Formula and explanation:** The p

1. **State the problem:** Solve the equation $1.2 \times 46 = 72 \times 48$ for verification or simplification. 2. **Calculate each side:**

1. **State the problem:** Solve the equation $$3|x - 5| = 12$$ for $$x$$. 2. **Isolate the absolute value:** Divide both sides by 3 to get $$|x - 5| = \frac{12}{3}$$.

1. The problem is to solve the equation $|x| = 2$. 2. Recall that the absolute value $|x|$ represents the distance of $x$ from zero on the number line, so $|x| = a$ means $x = a$ o

1. **State the problem:** Factor the trinomial $$x^2 + 7x + 12$$. 2. **Formula and rules:** To factor a trinomial of the form $$x^2 + bx + c$$, find two numbers that multiply to $$

1. The problem involves understanding the relationships between variables $b$ and $m$ given by three equations and their corresponding tables and graphs. 2. The first equation is $

1. The problem asks for an expression representing the distance a fish swims in $x$ hours, given its speed is 12 miles per hour. 2. The formula for distance when speed and time are

1. **State the problem:** Solve the system of equations by substitution: $$y = -x$$

1. **State the problem:** Solve the system of equations by substitution: $$y = -4x$$

1. **State the problem:** Simplify the expression $$\frac{3x}{x-2} \times \frac{x}{2x+4} \times \frac{5}{x}$$. 2. **Recall the rules:** When multiplying fractions, multiply the num

1. **State the problem:** Simplify the expression $$\frac{x}{x^2-1} - \frac{x-3}{x-1}$$. 2. **Recall the formula and rules:** The denominator $x^2-1$ can be factored using the diff

1. **State the problem:** Simplify the expression $$\frac{x}{x^{2-1}} - \frac{x-3}{x-1}$$. 2. **Rewrite the powers:** Note that $$x^{2-1} = x^1 = x$$, so the first fraction becomes

1. **State the problem:** Simplify the expression $$\frac{x}{x^2-1} - \frac{x-3}{x-1}$$. 2. **Recall the formula and rules:**

1. **State the problem:** Simplify the expression $$\frac{3x+4}{x} - \frac{5}{6x} + \frac{9}{2x}$$. 2. **Identify the common denominator:** All terms have denominators involving $x

1. **State the problem:** Simplify the expression $$\frac{3x+4}{x} - \frac{5}{6x} + \frac{9}{2x}$$. 2. **Identify the common denominator:** All terms have denominators involving $x

1. **State the problem:** Simplify the expression $$\frac{3x+4}{x} - \frac{5}{6x} + \frac{9}{2x}$$. 2. **Identify the common denominator:** All terms have denominator involving $x$

1. **State the problem:** Simplify the expression $$\frac{3x+4}{x} - \frac{5}{6x} + \frac{9}{2x}$$. 2. **Identify the common denominator:** The denominators are $x$, $6x$, and $2x$