🧮 algebra

1. Let's clarify the step where division was performed. 2. When dividing an expression, the sign of the first number can be negative; division rules apply as usual.

1. **State the problem:** Solve the equation $$30 = 18x - 2x^2$$ for $x$. 2. **Rewrite the equation:** Move all terms to one side to set the equation to zero:

1. The problem is to factorize the expression given by the equation $$0 = 09 - 8t \times xe$$. 2. First, simplify the constant term: $$09 = 9$$, so the equation becomes $$0 = 9 - 8

1. **State the problem:** A gardener has 18 metres of timber fencing to enclose a rectangular vegetable patch using a stone wall as one side. The width of the patch is $x$ metres.

1. **State the problem:** Simplify the expression $$3 + \frac{(9 - 1)}{4}$$ using the order of operations (PEMDAS). 2. **Recall the order of operations:** Parentheses first, then E

1. **State the problem:** Simplify the expression $2 + (6 \div 6) \times 8$ using the order of operations (PEMDAS). 2. **Recall the order of operations:** Parentheses, Exponents, M

1. The problem asks to create a table for the reflection about the origin of the function $f(x) = (x + 2)^2 + 1$. 2. The reflection about the origin of a function $f(x)$ is given b

1. **State the problem:** We want to simplify the expression $e^{\ln a^x}$. 2. **Recall the properties of logarithms and exponentials:** The natural logarithm $\ln$ and the exponen

1. **State the problem:** Add the fractions $\frac{1}{2}$ and $\frac{4}{5}$. 2. **Formula:** To add fractions, use the formula $$\frac{a}{b} + \frac{c}{d} = \frac{ad + bc}{bd}$$ wh

1. The problem is to multiply the numbers $2$, $-\frac{2}{3}$, and $\frac{3}{4}$.\n\n2. The multiplication rule for fractions and integers is to multiply the numerators together an

1. **Problem Statement:** We want to find pairs of numbers from the set $\{1, 2, 2, 2, 3, 4, 4, 5, 5, 6, 6, 6, 7, 7, 7, 8, 8, 8, 8, 9\}$ that can produce the numbers in the set $\{

1. The problem is to understand how to factor algebraic expressions. 2. Factoring means rewriting an expression as a product of simpler expressions.

1. The problem asks for the domain of the function $(q \circ r)(x)$, which means the composition of functions $q$ and $r$. 2. The domain of $(q \circ r)(x)$ is all $x$ values in th

1. **State the problem:** We are given two functions: $$q(x) = \frac{1}{x - 8}$$

1. The problem is to add the fractions $\frac{1}{5}$ and $\frac{2}{5}$.\n\n2. When adding fractions with the same denominator, you add the numerators and keep the denominator the s

1. **State the problem:** Simplify the expression $$\frac{2}{3} \times \frac{4}{5}$$. 2. **Recall the rule for multiplying fractions:** Multiply the numerators together and the den

1. The problem asks to predict the amount after 50 days using the best fitting curve, which is given as Figure 3: $$y = 546(0.98)^x$$. 2. The formula for exponential decay is $$y =

1. **State the problem:** Solve the inequality $$(x + 2)(x - 3)(x + 3)(x + \geq 0$$ (assuming the last factor is $(x + 1)$ due to typo). 2. **Rewrite the inequality:**

1. **State the problem:** Given $a = \frac{1+\sqrt{5}}{2}$, find the value of $a^6 - 8a^2$. 2. **Recall the formula and properties:** The number $a = \frac{1+\sqrt{5}}{2}$ is the g

1. **State the problem:** Find the domain of the function $$y = -\sqrt{x}$$. 2. **Recall the domain rule for square root functions:** The expression inside the square root must be

1. **State the problem:** Find the domain of the function $$y = \sqrt[3]{x - 1}$$. 2. **Recall the domain rule for cube root functions:** The cube root function $$\sqrt[3]{x}$$ is