🧮 algebra

1. **State the problem:** Solve the equation $$-6 + \frac{x}{2} = -3$$ for $x$. 2. **Isolate the variable term:** Add 6 to both sides to move the constant term.

1. **State the problem:** Solve the inequality $$\frac{x}{9} - \frac{x}{7} < 0$$. 2. **Find a common denominator:** The denominators are 9 and 7, so the common denominator is $$63$

1. **State the problem:** Evaluate the expression $5^2 - (7 - 2 \times 3)$. 2. **Recall order of operations:** Use PEMDAS (Parentheses, Exponents, Multiplication and Division from

1. **State the problem:** Evaluate the expression $5^2 - (7 - 2 \times 3)$. 2. **Recall order of operations:** Use PEMDAS (Parentheses, Exponents, Multiplication and Division (left

1. **State the problem:** Simplify the expression $9 - 3(9 - 3)$. 2. **Recall the order of operations:** Parentheses first, then multiplication, then addition/subtraction from left

1. The problem is to find the value of the given expression or quantity. 2. Since the user did not specify the exact expression, we need the expression to proceed.

1. **State the problem:** We need to find the equation that represents the proportional relationship between the number of pencils $p$ and the cost $c$ given the data points: $(9,

1. **State the problem:** We want to find the share of the customer's wallet spent at your store compared to the total amount spent on flower arrangements. 2. **Identify the given

1. Stating the problem: Solve the equation $$|x - |x|| = 10$$. 2. Understand the absolute value function: $$|x| = \begin{cases} x & \text{if } x \geq 0 \\ -x & \text{if } x < 0 \en

1. **State the problem:** Write an equation that represents the proportional relationship between the price $P$ of canned corn and the number of cans $c$ purchased. 2. **Analyze th

1. **State the problem:** Solve the system of linear equations: $$\frac{x}{6} - \frac{y}{2} = \frac{1}{6}$$

1. **State the problem:** We are given two ratios involving jellies, mints, and toffees: - Jellies to mints: $7n : 3$

1. **State the problem:** Solve the system of linear equations: $$-\frac{1}{4}x + 3y = 6$$

1. **State the problem:** Find the equation of the line in point-slope and slope-intercept form given points (-2, -5) and (5, 0). 2. **Find the slope $m$ using the formula:**

1. We are asked to solve an equation using substitution. 2. The substitution method involves replacing a complicated expression with a simpler variable to make the equation easier

1. **State the problem:** Solve the system of equations by substitution, clearing $x$: $$4x + 5y = 4$$

1. **State the problem:** Simplify the expression $$\frac{x^2 + 13x + 12}{x + 1} \times \frac{5x + 10}{4x^2 - 16}$$. 2. **Factor all polynomials:**

1. **Fill in the blanks in the table:** Percent | Fraction | Decimal

1. **Problem statement:** A parking garage charges $5 for the first hour, $10 for up to two hours, and $12 for the entire day. Let $G$ be the dollar cost of parking for $t$ hours.

1. **Problem Statement:** Evaluate the piecewise function $$f(x) = \begin{cases} -2x + 3, & x < -1 \\ 2x^2, & x \geq -1 \end{cases}$$

1. **State the problem:** Simplify the expression $$\frac{7^2 \times (-8)^{-5} \times 3^4}{7^5 \times 8^{-7} \times 3^3}$$. 2. **Recall the rules:**