🧮 algebra

1. **State the problem:** Solve the equation $x + \log_2(2^x - 6) = 4$ for $x$. 2. **Rewrite the logarithmic expression:** Recall that $\log_2(2^x) = x$. Here, the argument inside

1. **State the problem:** Solve the system of linear equations: $$-10x = -10$$

1. **State the problem:** Solve the system of linear equations: $$2x - 8y = -10$$

1. **State the problem:** Solve the system of linear equations: $$2x - 8y = -10$$

1. **Expand and simplify** the expression $(x + 5)(x + 4)(x - 3)$ to find constants $A$, $B$, $C$, and $D$. Start by expanding two brackets first:

1. **Evaluate the expression:** $$6 - 6 \times (-6)^3 \div 7$$ 2. Calculate the power: $$(-6)^3 = -216$$

1. The problem asks us to determine which inequalities among A, B, C, and D are true. 2. Evaluate each inequality:

1. The problem asks which number is located to the right of the point $-3.27$ on the number line. 2. Numbers to the right of $-3.27$ must be greater than $-3.27$.

1. Let's analyze each statement to determine if it is true or false. 2. Statement: "0 is neither a rational number nor an irrational number."

1. Let's analyze each statement to determine its truth value. 2. Statement: "0 is neither a rational number nor an irrational number."

1. **State the problem:** Simplify the expression $$|3 - 8| - \left(\frac{12}{3} + 1\right)^2$$. 2. **Calculate the absolute value:** $$|3 - 8| = |-5| = 5$$.

1. The problem asks for the opposite of 145. 2. The opposite of a number $x$ is defined as $-x$.

1. The problem states: If the absolute value of $x$ is 12, which of the following is true? 2. Recall the definition of absolute value: $|x| = 12$ means the distance of $x$ from 0 o

1. The problem asks to find the value of $|6| - |-6| - (-6)$.\n\n2. Recall that the absolute value $|x|$ is the distance of $x$ from zero on the number line, always non-negative.\n

1. **State the problem:** We want to analyze the function $$y=\frac{x^3+3x}{(x+1)(x+2)}$$ including simplification and key features. 2. **Simplify the numerator:** Factor out $x$ f

1. **Stating the problem:** Rearrange the formula $$W = \frac{h^2}{7x}$$ to make (a) $$h$$ the subject and (b) $$x$$ the subject. 2. **Rearranging for h:**

1. State the problem: Find the value of the expression $$(3x - 12) - \left(\frac{1}{2}xy - 10\right)$$ for $x=3$ and $y=6$. 2. Substitute the values of $x$ and $y$ into the express

1. **Problem statement:** We have two functions: an exponential function $f(x) = a^x + q$ with horizontal asymptote $y=3$, and a linear function $g(x) = mx + c$. They intersect at

1. The problem is to verify if the equation $$(7x+3)^2 = (7x+4)(7x-4)$$ is correct and solve for $x$ if it is. 2. First, expand both sides:

1. **State the problem:** Solve the equation $$(6x - 9)^2 - (3x - 5)^2 = (9x + 4)(3x + 2)$$ for $x$. 2. **Expand the squares using the formula $(a - b)^2 = a^2 - 2ab + b^2$:**

1. The problem is to solve the quadratic equation $$2x^2 - 4x - 6 = 0$$. 2. First, identify the coefficients: $$a = 2$$, $$b = -4$$, and $$c = -6$$.