🧮 algebra

1. The problem is to solve the equation $$-20 = -10x$$ for $x$. 2. The goal is to isolate $x$ by dividing both sides of the equation by the coefficient of $x$, which is $-10$.

1. **State the problem:** Solve the equation $$x - 5 = -3$$ for $x$. 2. **Recall the goal:** We want to isolate $x$ on one side of the equation to find its value.

1. **State the problem:** Simplify the expression $$\frac{\frac{3}{2} + \frac{3}{x}}{2 + \frac{4}{x}}$$. 2. **Rewrite the expression:** To simplify, first find a common denominator

1. **State the problem:** Solve the rational equation $$\frac{4}{3x+3} = \frac{12}{x^2-1}$$. 2. **Identify the denominators and restrictions:** The denominators are $3x+3$ and $x^2

1. **State the problem:** Expand the expression $$(4x^2 + y^4)^2$$ and write the answer as a polynomial in standard form. 2. **Recall the formula:** The square of a binomial $$(a +

1. **State the problem:** Factor the quadratic expression $x^2 - 12x + 20$. 2. **Recall the factoring formula:** For a quadratic $ax^2 + bx + c$, we look for two numbers that multi

1. The problem is to find the difference between 7 3/8 % and 6 7/8 %. 2. First, convert the mixed percentages to improper fractions or decimals for easier subtraction.

1. **State the problem:** Solve the system of equations: $$7.5a + 4b + 3.5c = 3025$$

1. **State the problem:** Solve the system of linear equations: $$\begin{cases} a + b + c = 22.3 \\ 3a - b - 6c = -11.8 \\ 2a + b - c = 24.7 \end{cases}$$

1. **State the problem:** Find two positive even consecutive integers such that the square of the smaller integer is 10 more than the larger integer. 2. **Define variables:** Let t

1. **State the problem:** Calculate the slope of the line passing through the points $(1400, 17)$ and $(1700, 14)$ where the horizontal axis represents calories and the vertical ax

1. **State the problem:** We have an outer rectangle with dimensions length $3x - 2$ and width $x + 6$, and an inner rectangle with dimensions length $2x$ and width $x - 1$. The sh

1. **State the problem:** The present ages of two friends add up to 50. Six years ago, one friend's age was twice the age of the other. 2. **Define variables:** Let the present age

1. **State the problem:** JimBob ran a 200-meter race 4 times. His two fastest times averaged 26.3 seconds, his slowest time was 30.3 seconds, and his overall average time was 28.0

1. **State the problem:** Divide the expression $$\frac{2x^4}{x^1}$$. 2. **Recall the rule for dividing powers with the same base:** When dividing terms with the same base, subtrac

1. Stating the problem: Solve the quadratic equation involving complex terms: $$4x^2 - 7ix = 3$$ 2. Rewrite the equation in standard quadratic form: $$4x^2 - 7ix - 3 = 0$$

1. **State the problem:** Given the function $f(x) = (x - 2)(2x - 12)$, find the y-intercept, x-intercepts, line of symmetry, vertex, value at $x = -1$, and intervals where the fun

1. **State the problem:** Solve the equation $$20x^2 - 6 = 13ix\sqrt{3}$$ for $x$. 2. **Rewrite the equation:** We want to isolate $x$. The equation is $$20x^2 - 6 = 13ix\sqrt{3}$$

1. **State the problem:** Find the slope $m$ of the line passing through points $P(0,0)$ and $Q(-1, \sqrt{3})$. 2. **Formula for slope:** The slope $m$ between two points $(x_1,y_1

1. **State the problem:** Simplify the algebraic expression $9x - 4y + 2x - y - 6x + 5y$. 2. **Identify like terms:** Like terms are terms that have the same variable raised to the

1. **State the problem:** Find the slope $m$ of the line passing through points $C(10,8)$ and $D(4,-4)$.\n\n2. **Formula:** The slope $m$ between two points $(x_1,y_1)$ and $(x_2,y