🧮 algebra

1. Solve the equation: $$4a + 9a - 6a = 42$$ 2. Combine like terms on the left side:

1. **State the problem:** Solve the logarithmic equation $$\log_4(3x + 10) = 2$$. 2. **Recall the definition of logarithm:** If $$\log_b(a) = c$$, then $$a = b^c$$.

1. **State the problem:** Solve the logarithmic equation $$\log_4(2x) = \log_4(63 - x^2)$$. 2. **Recall the logarithm property:** If $$\log_a(M) = \log_a(N)$$ and the base $$a > 0,

1. **State the problem:** Simplify the expression $$10p - \frac{8}{p^2 - 50p + 44}$$ and express it as a single fraction in simplest form. 2. **Factor the denominator:** The quadra

1. **State the problem:** We have the system of equations: $$y = -1.5$$

1. **State the problem:** We have the quadratic expression $$4x^2 + bx - 45$$ where $$b$$ is a constant. It can be factored as $$(hx + k)(x + j)$$ where $$h, k, j$$ are integers. W

1. **State the problem:** The admission fee for a child $c$ is $4$ more than one-half the admission fee for an adult $a$. We want to find the total amount paid for 12 children and

1. **State the problem:** We need to find the expression that represents the perimeter of a triangle with side lengths labeled as $2b + 1$, $-4 + 3b$, and $b$. 2. **Recall the form

1. **State the problem:** Maggie has a 50 gift card and wants to buy games costing 1.99 each. She has a 5 off coupon for the entire purchase. We need to find an equation to represe

1. **State the problem:** We need to find an equation to represent the total area covered by employee offices and the break room. 2. **Identify given information:**

1. **State the problem:** Simplify the expression $$\frac{(xyz^2)^{-1}}{x^2y^{-1}z^3} \div \left(\frac{x^3y^2z^0}{x^4y^2z^{-3}}\right)^{-1} \times \frac{xy^2z^4}{x^{-3}y^2z^0}$$

1. **State the problem:** Simplify the expression $$\frac{8}{3v-6} + \frac{6v}{v+3}$$. 2. **Identify the denominators and factor if possible:**

1. **State the problem:** Simplify the expression $$\frac{x^a y^{2a}}{x^{2a-1}} \div \frac{(x^2 y)^a}{x^{3+a} y^{-1}}$$. 2. **Rewrite the division as multiplication by the reciproc

1. **State the problem:** Find the equation of the line passing through the points $(-4, 6)$ and $(-2, 0)$. 2. **Formula used:** The slope $m$ of a line through points $(x_1, y_1)$

1. **State the problem:** We need to find the value of the composition \((f \circ g)(-2)\), which means \(f(g(-2))\). 2. **Identify given functions and values:**

1. **State the problem:** We need to order the numbers 20.85, -20.04, 20.75, and 20 from greatest to least. 2. **Recall the rule:** When ordering numbers from greatest to least, th

1. **State the problem:** Solve the inequality $$\left|\left(\frac{2}{5}\right)^x - \left(\frac{5}{2}\right)^{-2x}\right| < 2.$$\n\n2. **Rewrite the terms:** Note that $$\left(\fra

1. The problem is to find a formula that directly gives the answer to a given question without intermediate steps. 2. To provide a direct formula, you need to know the type of prob

1. **State the problem:** Solve the equation $$\frac{x - 2}{4} + \frac{x + 1}{2} = 1$$. 2. **Formula and rules:** To solve equations with fractions, find a common denominator to co

1. **State the problem:** We need to evaluate the expression $Y + \frac{x}{7} - 4$ given that $Y = -9$. 2. **Substitute the known value:** Replace $Y$ with $-9$ in the expression:

1. **State the problem:** Given the equation $y=\frac{x}{-3}-1$ and $x=27$, find the value of $y$. 2. **Formula used:** The equation is already given as $y=\frac{x}{-3}-1$.