🧮 algebra

1. **State the problem:** Solve the linear equation $4x - 7 = 7x + 5$ for $x$. 2. **Write the formula and rules:** To solve for $x$, we want to isolate $x$ on one side. We do this

1. **State the problem:** We want to find a factor of the polynomial $$60x^4 + 56x^2 + 12$$ of the form $$ax^2 + b$$ where $$a$$ and $$b$$ are positive constants. Then, we need to

1. **State the problem:** Mai earns a fixed wage plus extra money for every hour of overtime she works. The graph shows her total pay (in dollars) versus the amount of overtime (in

1. The problem describes Deshaun walking to school at a constant rate, stopping midway, then continuing at a slower rate. 2. We need to choose the graph that best represents distan

1. The first problem is to simplify or factor the expression $x^2 + 6x + 8$. 2. We use the factoring formula for quadratic expressions: $$ax^2 + bx + c = (x + m)(x + n)$$ where $m$

1. **Problem statement:** Apply the distributive property to each expression to write an equivalent expression. 2. **Recall the distributive property:** For any expressions $a$, $b

1. **State the problem:** We are given two inequalities: $$y \leq \frac{7}{4}x + 3$$

1. Plantegem el problema: Resolem l'equació $$x(3x-1) + 2x(x+1) = 9 - 3(2-x)$$ per trobar els valors de $x_1$ i $x_2$. 2. Desenvolupem i simplifiquem cada costat de l'equació:

1. **State the problem:** Solve the quadratic equation $$6x - x(x - 13) = 18$$ for $x$. 2. **Rewrite the equation:** Expand the term $x(x - 13)$:

1. **Statement of the problem:** Solve the quadratic equation $$x^2 + 8x = 0$$. 2. **Rewrite the equation:** The equation can be factored by taking $$x$$ common:

1. **Problem 11:** What percent of this circle is shaded? Since the problem does not provide a specific fraction or angle of the shaded part, we cannot calculate the exact percenta

1. **State the problem:** Find the slope of the line passing through the points $(-2, 5)$ and $(4, -1)$. 2. **Formula for slope:** The slope $m$ between two points $(x_1, y_1)$ and

1. The problem asks to identify which scenario represents a proportional relationship. 2. A proportional relationship means the ratio between two quantities is constant and the gra

1. **State the problem:** Find the discriminant of the quadratic equation and determine how many real solutions it has. The equation is given as:

1. **State the problem:** Find the discriminant of the quadratic equation and determine how many real solutions it has. 2. **Rewrite the equation:** Given $7 = -9x^2$, rewrite it i

1. **State the problem:** Solve the system of equations for $y$ in terms of $x$: $$0 = -2y + 10 - 6x$$

1. **State the problem:** Solve the system of equations: $$4x + 2y = 10$$

1. **State the problem:** Simplify the expression $\frac{2x^2 - 8}{4x}$. 2. **Write the formula and rules:** To simplify a rational expression, factor numerator and denominator and

1. **Stating the problem:** We have a 4x4 grid with shapes in each cell and totals for each row and column. We need to find the missing column total marked with a question mark. 2.

1. **State the problem:** Factor the quadratic expression $x^2 + 14x + 45$. 2. **Recall the factoring formula:** For a quadratic expression $ax^2 + bx + c$, we look for two numbers

1. **State the problem:** Factor the quadratic expression $x^2 + 11x + 24$. 2. **Recall the factoring formula:** For a quadratic $ax^2 + bx + c$, we look for two numbers that multi