🧮 algebra

1. The problem asks to find the function rule for $g(x)$, which is a translation of the absolute value function $f(x) = |x|$. 2. The general form for a translated absolute value fu

1. **State the problem:** Solve the equation $$\frac{x + 6}{x - 5} = \frac{5}{4}$$ for $x$. 2. **Use the cross-multiplication method:** When two fractions are equal, their cross pr

1. **State the problem:** Solve the equation $$\frac{4}{x+6} = \frac{5}{4x-8}$$ for $x$ and simplify the answer fully. 2. **Use the cross-multiplication formula:** For equations of

1. **State the problem:** Simplify the expression $5x(x-1)-4(x+1)$. 2. **Apply the distributive property:** Multiply each term inside the parentheses by the factor outside.

1. **State the problem:** Convert the equation $2x - 3y = 5$ to slope-intercept form $y = mx + b$. 2. **Recall slope-intercept form:** The slope-intercept form is $y = mx + b$, whe

1. Stating the problem: Calculate the value of the expression $$\frac{\left(\frac{3}{7} + \frac{1}{2}\right)^2 \cdot \left(2 - \frac{1}{3}\right)^2 - 1}{\left(\frac{1}{6} - 1\right

1. Planteamos el problema: Tenemos la función $f(x) = \frac{2x}{2-x}$ y queremos encontrar la función compuesta $f(f(x))$. 2. Recordemos que la función compuesta $f(f(x))$ signific

1. **State the problem:** Find the slope $m$ of the line passing through the points $(-5,12)$ and $(9,-10)$ in the form $y=mx+b$. 2. **Formula for slope:** The slope $m$ between tw

1. **State the problem:** Gillian has three test scores. The first is 90, the second is 75, and the third is unknown. We want to find the lowest score on the third test so that the

1. **State the problem:** We want to find how much bigger 500 is compared to 450, expressed as a percentage. 2. **Understand the idea:** To find how much bigger one number is than

1. **State the problem:** We want to find what percent 500 is more than 450. 2. **Formula:** The percent increase from a number $a$ to a number $b$ is given by:

1. The problem is to determine if the final equation can be simplified further. 2. To simplify an equation, we look for common factors, like terms, or algebraic identities.

1. **State the problem:** John wants to find the distance at which the cost of renting a car from Long Hauler Rentals and Discount Rentals is the same. 2. **Define variables and wr

1. The problem asks to identify the independent and dependent variables in the statement: "As the elapsed time $t$ since a racecar leaves the starting line increases, the distance

1. **State the problem:** Determine if the given rule defines $y$ as a function of $x$ based on the pairs: $$\begin{array}{c|c}

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

1. The problem is to determine if the given equation is a trigonometric equation. 2. A trigonometric equation is an equation that involves trigonometric functions such as $\sin$, $

1. **State the problem:** We know that 50% of the children travel by bus, and this 50% corresponds to 500 children. We need to find the total number of children attending the schoo

1. The problem states that 80% of the days in April were sunny. We need to find how many days were sunny. 2. April has 30 days in total.

1. The problem asks to write the product $xy \cdot xy \cdot xy \cdot xy$ using exponents. 2. Recall the rule for exponents: when multiplying the same base, add the exponents. For e

1. **State the problem:** Solve the equation $$\frac{2x+4}{3} = 5$$ for $x$. 2. **Formula and rules:** To solve for $x$, multiply both sides of the equation by the denominator to e