🧮 algebra

1. The problem asks to express 143 cents in dollars. 2. We know that 100 cents equal 1 dollar.

1. Stating the problem: Solve the equation $$\frac{X}{20} - 5 = -4$$ for $X$. 2. Add 5 to both sides to isolate the fraction term:

1. Stating the problem: Solve for $X$ in the equation $$\frac{X}{8} + 4 = 12$$. 2. Formula and rules: To isolate $X$, we first need to eliminate the constant term on the left side

1. **State the problem:** Solve the equation $$\frac{3}{x-2} - \frac{6}{x^2-4} = \frac{2}{x^2-1}$$. 2. **Identify excluded values:** The denominators cannot be zero, so exclude val

1. **Problem:** Write equations for the lines shown on the graph. 2. **Step 1: Find the equation of the first line passing through points (-6,0) and (0,6).**

1. The problem is to solve a system of linear equations by graphing. 2. To solve by graphing, we first write each equation in slope-intercept form $y=mx+b$ where $m$ is the slope a

1. The problem is to solve the system of equations: $$y = -x - 2$$

1. **State the problem:** Solve the equation $$\frac{5x}{2} = 11 + \frac{2x}{3}$$ for $x$. 2. **Identify the goal:** We want to isolate $x$ on one side of the equation.

1. **State the problem:** Write an equation in slope-intercept and standard form that passes through the point $(5, -5)$ and is parallel to $y = -\frac{7}{5}x - 5$. 2. **Identify t

1. **State the problem:** We have a polygon with edges and angles, and three pairs of congruent edges: - $15x + 17 = 3z - 5$

1. **State the problem:** Simplify the expression involving powers of $g$ given as $$\frac{g(x)}{g^9} = \frac{4}{g^9}$$ and related expressions using exponent rules. 2. **Recall th

1. **State the problem:** Find the equation of a graph that is a horizontal line with a y-intercept of -3. 2. **Recall the formula for a horizontal line:**

1. **Problem:** Multiply and simplify the radicals for the first expression: $$\sqrt{6}^3 \cdot \sqrt{8}r^2$$ 2. **Recall:** The product of radicals rule: $$\sqrt{a} \cdot \sqrt{b}

1. **State the problem:** Solve the rational equation $$\frac{5}{x+1} + \frac{1}{x-1} = \frac{x}{x-1}$$ for all values of $x$. 2. **Identify restrictions:** The denominators cannot

1. **Problem:** Factor out the GCF from $14r^2s^3 + 20r^3s - 10r^4s^5$. 2. **Step 1:** Identify the GCF of the coefficients: GCF of 14, 20, and 10 is 2.

1. **State the problem:** Solve the rational equation $$1 + \frac{2}{x - 8} = \frac{x}{x^2 - 12x + 32}$$ for all values of $x$. 2. **Factor the denominator on the right side:** Not

1. **State the problem:** We need to find the coordinates of the vertices of the triangle formed by the intersection of the three lines: $$y = x + 1$$

1. **State the problem:** Solve the equation $$5 \left(\frac{x}{3}\right)^2 - 3 \left(\frac{1}{9}\right) = - \frac{8}{9}$$ for $x$. 2. **Recall the formula and rules:** We will sim

1. **State the problem:** We need to find the coordinates of the vertices of the triangle formed by the intersection of the three lines: $$y = x + 1$$

1. **State the problem:** Solve the inequality $3b \leq 9$ and graph it on the number line. 2. **Formula and rules:** To solve inequalities, isolate the variable by performing inve

1. **State the problem:** Solve the equation $ (x - 9)(x + 2) = (x + 4)(x - 7) $ for $x$. 2. **Expand both sides:** Use the distributive property (FOIL) to expand each product.