🧮 algebra

1. **State the problem:** We need to solve the equation $$\frac{2x+4}{x-1} = 3$$ for $x$. 2. **Recall the formula and rules:** To solve a rational equation like this, multiply both

1. **State the problem:** Solve the quadratic equation $$7r^2 - 14r = -7$$. 2. **Rewrite the equation:** Move all terms to one side to set the equation to zero:

1. The problem appears to be a set of fractions: $\frac{9}{4}$, $\frac{11}{2}$, $\frac{11}{3}$, and $\frac{11}{4}$. We will simplify or compare these fractions. 2. To compare or si

1. **State the problem:** We need to find the input values $x$ such that $t(x) = 12$ and $t(x) = 17$ for the function $$t(x) = 5x^2 - 3x + 4.$$ 2. **Use the formula:** Set the func

1. **State the problem:** Solve the equation $$2 = 3^{0.01t}$$ for $t$. 2. **Recall the formula and rules:** To solve for $t$ when it is in the exponent, use logarithms. The key pr

1. The problem is to find the values of $x$ for which $r(x) = 9.3$ and $r(x) = 20$ given the function $r(x) = 5 \ln(1.4)(1.4^x)$. 2. The function is given as $r(x) = 5 \ln(1.4)(1.4

1. **State the problem:** Factor the polynomial $$4x^3 - x^2 + 8x - 2$$ by grouping. 2. **Group terms:** Group the polynomial into two pairs:

1. **State the problem:** Factor the polynomial $$6m^3 + 5mn + 6m^2 + 5n$$ by grouping. 2. **Group terms:** Group the polynomial into two pairs:

1. **State the problem:** Factor the polynomial $$4x + 16 + xy + 4y$$ by grouping. 2. **Group terms:** Group the polynomial into two pairs:

1. **State the problem:** Determine if the relation given by the arrow diagram is a function. 2. **Recall the definition of a function:** A relation is a function if every input (d

1. **State the problem:** Factor the polynomial $$-12a^4 + 9a^3 - 3a^2$$ completely, including factoring out a negative number or a GCF with a negative coefficient. 2. **Identify t

1. **Problem a:** Find the point of intersection of the lines $y=2x-1$ and $y=-x+8$. 2. To find the intersection, set the two expressions for $y$ equal:

1. **State the problem:** Factor the polynomial $$-7x - 35$$ by factoring out the greatest common factor (GCF) with a negative coefficient. 2. **Identify the GCF:** The terms are $

1. **State the problem:** Simplify the expression $z(y + 7) - 8(y + 7)$. 2. **Identify the common factor:** Both terms contain the factor $(y + 7)$.

1. **State the problem:** We are given four data points that suggest an exponential decay pattern: 16,510.34, 13,266.81, 10,778.49, and 8,774.27. 2. **Identify the exponential func

1. **State the problem:** Find the solution to the system of linear equations: $$y = -2x - 9$$

1. **State the problem:** Factor the polynomial $$\frac{1}{6}x^9 + \frac{5}{6}x^8 - \frac{7}{6}x^7 + \frac{1}{6}x.$$ 2. **Identify common factors:** Each term has a factor of $$\fr

1. The problem is to find the common ratio (base) of an exponential function that models the data points for money in an account: $144.07$, $374.53$, $605.68$, and $834.53$. 2. An

1. The problem is to simplify the expression $ (7y)^{\frac{1}{3}} $ using the power of a product property. 2. The power of a product property states that $ (ab)^n = a^n b^n $ for a

1. The problem asks to simplify the expression $\left(9^{\frac{1}{4}}\right)^{\frac{7}{2}}$ using the power of a power property. 2. The power of a power property states that $\left

1. **Problem Statement:** Solve the system of linear equations: $$\begin{cases} x + 3y = 12 \\ 2x + y = 6 \end{cases}$$