🧮 algebra

1. **State the problem:** Convert the equation $$y - 6 = 3(x + 2)$$ to slope-intercept form, which is $$y = mx + b$$ where $$m$$ is the slope and $$b$$ is the y-intercept. 2. **Use

1. **State the problem:** We need to find the point-slope form of the equation of a line given two points: $(0, -1)$ and $(4, 2)$. 2. **Recall the point-slope formula:** The point-

1. **State the problem:** Simplify the expression $$-\frac{1}{4} \times \left(-\frac{3}{5}\right) \times \left(-\frac{2}{3}\right)$$. 2. **Recall the multiplication of fractions ru

1. **State the problem:** Solve the equation $$ (2x+3)^2 - 9 = 0 $$. 2. **Rewrite the equation:**

1. The problem is to determine if $x = -19$ is a valid solution or to understand the context of $x = -19$. 2. Since no equation or context is given, we treat $x = -19$ as a stateme

1. **State the problem:** Solve the equation $$-2(x + 10) = 92$$ for $$x$$. 2. **Use the distributive property:** Multiply $$-2$$ by each term inside the parentheses:

1. **Problem Statement:** We need to fill out the Distance column given values for $c$ and $d$. 2. **Understanding the variables:** Typically, in problems involving distance, $c$ a

1. **State the problem:** Celeste rides to work at $12$ mph and returns at $8$ mph. The total time for the round trip is $1$ hour. We need to find the distance from her home to wor

1. **State the problem:** Solve the equation $$\frac{3x+4}{7} = \frac{x+8}{3}$$ for $x$. 2. **Formula and rules:** To solve an equation with fractions, we can cross-multiply to eli

1. **State the problem:** Solve for $x$ in the equation $$\frac{3x + 4}{7} = \frac{1}{3}$$. 2. **Use the cross-multiplication formula:** When two fractions are equal, their cross p

1. **State the problem:** Solve the equation $$\frac{33}{x} = -3$$ for $$x$$. 2. **Formula and rules:** To solve for $$x$$ in a fraction equation $$\frac{a}{x} = b$$, multiply both

1. **State the problem:** We need to find whether the equation $$\frac{33}{x} = -3$$ has one solution, no solutions, or infinitely many solutions. 2. **Recall the formula and rules

1. **State the problem:** We need to solve the equation $$\frac{33}{x} = -3$$ and verify the solution. 2. **Solve for $$x$$:** Multiply both sides by $$x$$ to eliminate the denomin

1. **State the problem:** Solve for $x$ in the equation $$-\frac{6}{7} = \frac{12}{x}$$. 2. **Use the cross multiplication method:** When two fractions are equal, their cross produ

1. **State the problem:** Solve the equation $$\frac{x - 8}{x - 2} = \frac{7}{8}$$ for $x$ and simplify fully. 2. **Use the cross-multiplication formula:** When two fractions are e

1. **State the problem:** We need to find the value of the piecewise function $$f(x)$$ at $$x=5$$. 2. **Identify the correct piece:** Since $$5$$ satisfies $$-1 \leq 5 \leq 7$$, we

1. We start with the problem: Los de vergelijking $$z^2 - 4z + 7 + 4i = 0$$ op voor het complexe getal $z$. 2. Dit is een kwadratische vergelijking in $z$. De algemene vorm is $$az

1. **State the problem:** Solve the cubic equation $$x^{3}-3x^{2}-9x+11=0$$. 2. **Recall the general approach:** For cubic equations, one method is to try to find rational roots us

1. **State the problem:** We need to solve the cubic equation $$x^{3}-3x^{2}-9x+11=0$$ for $x$. 2. **Recall the general approach:** For cubic equations, we can try to find rational

1. **State the problem:** A painter can paint a whole wall in $x$ hours. We want to find the fraction of the wall she paints in 4 hours.

1. **Problem:** A cell phone company charges a monthly fee of $30 for the first 1000 text messages and 10 cents for each additional text message. Miriam’s bill for June is $35.70.