🧮 algebra

1. **Stating the problem:** We have a triangle with two equal sides each measuring $x+1$ meters and a base measuring $2x-1$ meters. The perimeter of the triangle is 17 meters.

1. Stating the problem: Solve for $p$ in the equation $p - \frac{4}{9}p = -\frac{7}{9}$.\n\n2. Combine like terms on the left side: $p - \frac{4}{9}p = \frac{9}{9}p - \frac{4}{9}p

1. **State the problem:** We have a grid with numbers 2, 16, 3, and 24 arranged in a 2x3 grid, and a 5 pointing to an unknown $x$. The note says there are 24 purple jelly beans and

1. The problem asks for the equation of a line parallel to the line given by $$y = 2x + 5$$ and passing through the point $$(1,0)$$. 2. Recall that parallel lines have the same slo

1. **State the problem:** Solve the system of linear equations: $$x + 2y = 7$$

1. **Problem:** Simplify the expression $3a^3b^2 - 5a^3b^2 - 2a^3b^2$. 2. **Formula and rules:** When subtracting or adding like terms, combine coefficients and keep the variables

1. **State the problem:** Solve the inequality $$4 > -8x$$. 2. **Recall the rule for inequalities:** When dividing or multiplying both sides of an inequality by a negative number,

1. **State the problem:** Solve the equation involving fractions: $$t - \frac{3}{4} = 1 \frac{1}{4}$$ 2. **Convert mixed numbers to improper fractions:**

1. **State the problem:** Solve the inequality $4 > -8x$ for $x$. 2. **Write the inequality:**

1. **State the problem:** Find the slope $m$ of Line 1 passing through points $(-9, 99)$ and $(6, -51)$. 2. **Formula for slope:** The slope $m$ between two points $(x_1, y_1)$ and

1. The problem is to simplify the given expression or equation. 2. To simplify, we look for common factors, combine like terms, and reduce fractions if any.

1. **Problem:** Divide $3x - 5x^3 + 2$ by $x + 4$ using polynomial long division. 2. **Write the division statement:**

1. **State the problem:** Solve the equation $$-\frac{4}{15} n + \frac{2}{3} = \frac{2}{5} n$$ for $n$. 2. **Write down the equation:** $$-\frac{4}{15} n + \frac{2}{3} = \frac{2}{5

1. The problem is to solve the equation $$\frac{s}{6} = 2.5$$ for $s$. 2. The formula used here is to isolate $s$ by multiplying both sides of the equation by 6, the denominator of

1. **State the problem:** We need to find the slopes of two lines given two points on each line and then determine if the lines are parallel, perpendicular, or neither. 2. **Formul

1. **State the problem:** Ezra runs some distance $d$ miles, then has $\frac{1}{2}$ mile left to run, and the total distance he planned to run is $\frac{3}{4}$ mile. We want to fin

1. **State the problem:** Solve the system of equations: $$y = -\frac{3}{2}x + 3$$

1. **State the problem:** Solve the equation $$\frac{3}{4} - \frac{1}{2}b = -3b$$ for $b$. 2. **Rewrite the equation:** We want to isolate $b$. The equation is $$\frac{3}{4} - \fra

1. The problem is to solve the equation for $x$ given that each person gets $\frac{1}{4}$ of a gallon of lemonade. 2. We are given four possible equations:

1. **State the problem:** We have an exponential decay model for bacteria count given by $$B_{second}(t) = 6000 \cdot \left(\frac{15}{16}\right)^t$$ where $t$ is in seconds. 2. **I

1. **State the problem:** Solve the equation $$\frac{3}{8}m + \frac{7}{8} = 2m$$ for $m$. 2. **Identify the goal:** We want to isolate $m$ on one side of the equation.