🧮 algebra

1. **State the problem:** We need to find the number $x$ such that eight times the number plus 4 equals -4. 2. **Write the equation:**

1. **State the problem:** We need to find the markup $M$ given the retail price $P$ and the wholesale cost $C$. 2. **Formula:** The retail price is given by $$P = C + M$$ where $P$

1. The problem asks to fill in the blank: "A(n) ________ of an equation is a value for the variable that makes the equation a true statement." 2. Let's analyze the options:

1. **State the problem:** Determine the correct value of the expression $6 + 2x$ when $x=4$. 2. **Formula:** The expression is $6 + 2x$.

1. **State the problem:** Evaluate the expression $6 + 2x$ for $x = 4$. 2. **Formula:** The expression is $6 + 2x$.

1. The problem asks to find the number $x$ such that six times the difference of 11 and $x$ equals -72. 2. Write the equation: $6(11 - x) = -72$.

1. The problem asks to find the number $x$ such that six times the difference of 11 and $x$ equals -72. 2. Write the equation: $6(11 - x) = -72$.

1. **Stel het probleem vast:** We moeten het stelsel oplossen: $$\begin{cases} 5x + 2y = 4 - z \\ -3x - 6 = 4y - 5z \\ 8z = x + y + 1 \end{cases}$$

1. The problem states: "Six times the difference of 11 and a number is -72." We need to write this as an equation using $x$ to represent the number. 2. The phrase "difference of 11

1. **State the problem:** Solve the equation $$\frac{1}{4} t = -9$$ for $$t$$. 2. **Formula and rule:** To isolate $$t$$, multiply both sides of the equation by the reciprocal of $

1. The problem asks to write the sentence "The difference of -42 and 8 is -50" as an equation. 2. "Difference" means subtraction, so we subtract 8 from -42.

1. **State the problem:** Solve the equation $$3(x + 5) = 12$$ for $$x$$. 2. **Use the distributive property:** Multiply 3 by each term inside the parentheses.

1. The problem asks to find the area of a square with side length $9x$ centimeters. 2. The formula for the area of a square is:

1. **State the problem:** We need to find the number $x$ such that four times the sum of the number plus 2 equals eight times the number minus 28. 2. **Write the equation:** The pr

1. **State the problem:** Solve the equation $$21 = 3x - 3$$ for $$x$$. 2. **Add 3 to both sides** to isolate the term with $$x$$:

1. **State the problem:** Evaluate the expression $$\frac{7x + 2}{2y}$$ when $$x = 4$$ and $$y = -5$$. 2. **Write the formula:** The expression is $$\frac{7x + 2}{2y}$$.

1. The problem asks if the number 12 is a solution to the equation $k - 9 = 3$. 2. To check, substitute $k = 12$ into the equation.

1. The problem states: "A number added to -11 amounts to -25." We need to write this as an equation using $x$ to represent the number. 2. The phrase "a number added to -11" transla

1. **State the problem:** We need to find a number such that six times the number plus 8 equals 32. 2. **Write the equation:** Let the number be $x$. The equation is:

1. **State the problem:** Solve the equation $$-1(t - 8) = 4$$. 2. **Apply the distributive property:** Multiply $$-1$$ by each term inside the parentheses.

1. **State the problem:** Multiply the expression $$\frac{1}{2}(-8y - 4)$$. 2. **Formula and rules:** When multiplying a fraction by a sum, distribute the fraction to each term ins