🧮 algebra

1. The problem is to solve the equation $10 \div x = 45 \div 27$ for $x$. 2. First, rewrite the division as fractions: $\frac{10}{x} = \frac{45}{27}$.

1. **State the problem:** Solve the inequality $$\frac{n}{2} - 4 < 17$$. 2. **Isolate the term with $n$:** Add 4 to both sides to get rid of the $-4$ on the left.

1. **State the problem:** Solve the simultaneous equations: $$6y + 7x = 57$$

1. The problem is to solve the inequality $$9 > u - 4$$ for the variable $u$. 2. To isolate $u$, add 4 to both sides of the inequality:

1. **State the problem:** Solve the inequality $x + 6 \geq 4$. 2. **Isolate $x$:** Subtract 6 from both sides to get

1. **State the problem:** We are given two equations based on the cost of purses and watches:

1. **State the problem:** We are given two equations based on the cost of purses and watches:

1. **State the problem:** Solve the inequality $$3k + 8 \geq 26$$. 2. **Isolate the variable term:** Subtract 8 from both sides to get $$3k \geq 26 - 8$$.

1. **State the problem:** Solve the simultaneous equations: $$7x - 6y = 30$$

1. **State the problem:** We want to decompose the rational function $$\frac{5}{(x+2)^2(x+1)}$$ into partial fractions. 2. **Set up the partial fraction form:** Since the denominat

1. **State the problem:** Solve the inequality $$5w + 8 \leq 3w + 14$$. 2. **Isolate the variable terms:** Subtract $$3w$$ from both sides to get all $$w$$ terms on one side:

1. State the problem: Solve the inequality $\frac{a}{4} < 12$. 2. To isolate $a$, multiply both sides of the inequality by 4 (since 4 is positive, the inequality direction remains

1. **State the problem:** We know the cost of 2 buckets and 3 spades is 7. 2. **Express the problem mathematically:** Let the cost of one bucket be $b$ and one spade be $s$. Then:

1. The problem is to express the inequality shown on the number line. 2. The number line shows an open circle at 4, meaning the value 4 is not included.

1. The problem is to simplify the expression $\sqrt{x}2\sqrt{x}2\sqrt{x}2$. 2. First, rewrite the expression clearly: $\sqrt{x} \times 2 \times \sqrt{x} \times 2 \times \sqrt{x} \t

1. The problem is to simplify the expression $$\sqrt{x}(11 - 6\sqrt{x})^2 + \sqrt[n]{x}(11 + 6\sqrt{x})^2$$. 2. First, expand each squared term using the formula $$(a - b)^2 = a^2

1. Problem 84: Simplify the expression Given:

1. **Stating the problem:** Solve the quadratic equation $$221 - 12x + x^2 = 81$$ and analyze the given trigonometric identities. 2. **Rewrite the quadratic equation:** Move all te

1. The problem is to understand the graph of the inequality $$0^\circ \leq 1 \leq 360^\circ$$. 2. Here, the inequality compares the number 1 with the angles 0 degrees and 360 degre

1. **State the problem:** A bookstore owner buys 10 books for 900 when the price of each book increases by 3 Birr. We need to find the original price of one book. 2. **Define varia

1. **State the problem:** Perform long division on the product \((x-1)(x^3 - 70x^2 - 1203x - 1134)\). 2. **First, expand the product:**