🧮 algebra

1. **State the problem:** We need to analyze and understand the function $$f(x) = -|2x + 1|$$ and find some values to plot its graph. 2. **Recall the absolute value function:** The

1. **State the problem:** Solve the equation $-5 + 10X = 15X$ for $X$. 2. **Write the formula and rules:** To solve for $X$, we want to isolate $X$ on one side of the equation. We

1. **State the problem:** Solve the equation $-4X - 4 = -28X$ for $X$. 2. **Write down the equation:**

1. **State the problem:** Solve the equation $32 - 4X = 12X$ for $X$. 2. **Write down the formula and rules:** To solve for $X$, we need to isolate $X$ on one side of the equation

1. **State the problem:** Solve the equation $2x + 5 = 17x$ for $x$. 2. **Formula and rules:** To solve linear equations, we isolate the variable on one side by performing inverse

1. **State the problem:** Solve the equation $2X + 5 = 1X$ for $X$. 2. **Write down the equation:**

1. **State the problem:** Solve the equation $32 - 4x = 12x$ for $x$. 2. **Use the formula:** To solve linear equations, we isolate $x$ by moving all $x$ terms to one side and cons

1. The problem is to analyze and understand the function $$f(x) = |x - 1| + 2$$ and describe its graph. 2. The absolute value function $$|x - 1|$$ represents the distance of $$x$$

1. **State the problem:** Solve the equation $-x + 5 = 9x$ for $x$. 2. **Formula and rules:** To solve linear equations, we isolate the variable on one side by performing inverse o

1. **State the problem:** We are given the function $f(x) = \sqrt{3 - x} - 1$ and need to understand its behavior and plot its values. 2. **Formula and domain:** The function invol

1. **State the problem:** Norway has had three times as many rulers as Liechtenstein. The total number of rulers for both countries is 56. We need to find the number of rulers for

1. **State the problem:** Solve the equation $$-2(y + 4) = 2$$ for the variable $y$. 2. **Use the distributive property:** Multiply $-2$ by each term inside the parentheses.

1. **State the problem:** Determine if 7 is a solution to the equation $$7x = 56 - x$$. 2. **Substitute the value:** Replace $$x$$ with 7 in the equation:

1. **State the problem:** Solve the equation $$2x - (-0.3) = 1.9$$. 2. **Rewrite the equation:** Subtracting a negative is the same as adding a positive, so rewrite as:

1. The problem asks if the number 2 is a solution to the equation $3 - p = 1$. 2. Substitute $p = 2$ into the equation to check.

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

1. The problem asks to write the phrase "A number divided by 60" as a variable expression using $x$ to represent "a number." 2. The phrase "A number divided by 60" means we take th

1. **State the problem:** Solve the equation $$8(y + 6) = 10y + 48$$. 2. **Apply the distributive property:** Multiply 8 by both terms inside the parentheses.

1. **State the problem:** Solve the linear equation $$\frac{1}{3}x + 4 = 2$$. 2. **Isolate the variable term:** Subtract 4 from both sides to get $$\frac{1}{3}x + 4 - 4 = 2 - 4$$ w

1. The problem asks us to write the sentence "The product of -11 and -7 gives 77" as an equation. 2. "Product" means multiplication, so we multiply -11 and -7.

1. **State the problem:** Solve the linear equation $$-\frac{1}{5}r = 2$$ for $r$. 2. **Formula and rules:** To solve for $r$, we need to isolate $r$ by undoing the multiplication