🧮 algebra

1. **State the problem:** Convert the mixed number $2 \frac{4}{5}$ to an improper fraction in simplest form. 2. **Recall the formula:** To convert a mixed number $a \frac{b}{c}$ to

1. **State the problem:** We need to find which section of the graph represents all solutions to the system of inequalities: $$y \geq 7x$$

1. **State the problem:** We need to find which section of the graph represents all solutions to the system of inequalities: $$y \geq x + 4$$

1. **State the problem:** Simplify the expression $$\frac{7b^{2}c + 14bc}{7bc}$$. 2. **Write the formula and rules:** To simplify a fraction, factor the numerator and denominator a

1. **State the problem:** We need to find three numbers from the list $0.492$, $0.78$, $2.33$, $0.594$, $1.345$, and $0.076$ whose sum is exactly $3$. 2. **Approach:** We will chec

1. **State the problem:** Solve the equation $$x^{2/3} + (8x)^{1/3} = 24$$ for $x$. 2. **Rewrite the equation using substitution:** Let $$y = x^{1/3}$$. Then $$x^{2/3} = (x^{1/3})^

1. **State the problem:** We need to factor out the negative common monomial factor with the largest absolute value from the polynomial $$6 + 15x - 3x^2$$ and then write the result

1. **State the problem:** Factor out the greatest common monomial factor from the polynomial $$11y^3 - 22y^2 + 11y^2$$. 2. **Identify the terms:** The polynomial has three terms: $

1. **State the problem:** We know the engine loses $4.2$ horsepower due to friction, which represents $6\%$ of the total horsepower rating. We need to find the total horsepower rat

1. **State the problem:** We are given the equation $$h(-3x - 9) = -9(x + 9)$$ and need to find the value of $$h$$ for which the equation has zero solutions. 2. **Rewrite the equat

1. **State the problem:** We are given the equation $$h(-2x + 6) = -14(x - 2)$$ and asked to find the value of $$h$$ for which the equation has zero solutions. 2. **Rewrite the equ

1. **State the problem:** We are given the equation $$-8 (x + 2) = h (-x - 2)$$ and need to find the value of $h$ such that the equation has exactly one solution. 2. **Rewrite the

1. **State the problem:** We are given the equation $$-\frac{3}{2}x - 2 = hx + 4$$ and asked to find the value of $h$ for which the equation has zero solutions. 2. **Recall the rul

1. **State the problem:** Solve the equation $$2 - 2(-x + 1) = -3 + \frac{1}{2} (4x + 6)$$ for $$x$$. 2. **Distribute the terms:**

1. **State the problem:** Solve the equation $$2(4x + 3) + 4 = -2(-4x - 6) - 2$$ for $$x$$. 2. **Apply the distributive property:**

1. **State the problem:** Solve the equation $$3(-4x + 7) = 24x - 32$$ for $$x$$. 2. **Apply the distributive property:** Multiply $$3$$ by each term inside the parentheses.

1. **State the problem:** Simplify the expression $$\left(\frac{5de^{7}}{2e^{3}}\right) \times \left(\frac{4d^{2}ef^{17}}{def^{6}}\right)$$. 2. **Write the expression clearly:**

1. **State the problem:** We are given three points on a straight line: $(3,3)$, $(x,y)$, and $(6,9)$. We need to find an equation relating $x$ and $y$. 2. **Recall the formula for

1. **State the problem:** We need to find the values of $x$ that satisfy the equation $$(3x - 1)(x - 5) = 0$$. 2. **Recall the zero product property:** If the product of two factor

1. **State the problem:** Solve the quadratic equation $$12 - 8w + w^2 = 0$$. 2. **Rewrite the equation in standard form:** The standard form of a quadratic equation is $$aw^2 + bw

1. **State the problem:** Factor the trinomial $$5x^2 + 29x + 20$$. 2. **Recall the factoring method for trinomials:** For a quadratic in the form $$ax^2 + bx + c$$, we look for tw