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Questions tagged [algebra-precalculus]

For questions about algebra and precalculus topics, which include linear, exponential, logarithmic, polynomial, rational, and trigonometric functions; conic sections, binomial, surds, graphs and transformations of graphs, solving equations and systems of equations; and other symbolic manipulation topics.

This tag is for questions typically taught in precalculus, as well as elementary algebra.

These topics include linear, exponential, logarithmic, polynomial, rational, and trigonometric functions; conic sections, binomials, surds, graphs and transformations of graphs, solving equations and systems of equations; and other symbolic manipulation topics.

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Solve equation $\sqrt{4t + 1} = 3 - 3t$

Solve equation $\sqrt{4t + 1} = 3-3t$ → I squared both sides and got ► $4t + 1 = 9 - 18t- 3t²$ → I then moved the 3t² to the left side and combined like pairs and got ► $3t² + 12t - 8 = 0$ I'm stuck at that point. Can someone tell me what I am…
Kalina Kama
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Solve $2^{2x} + 9e^{-2x} = 6$ for x using substitution.

This is the equation I have: $$2^{2x} + 9e^{-2x} = 6$$ I want to solve for x using the substitution method. I've turned it into $$4^x+\frac{9}{e^{2x}} - 6 = 0$$ But I do not know what to substitute and how to solve it.
Just a guy
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Devise System of Equations to Solve Age Problem

Hi this may be simple silly problem but it is bugging me as I am not able to devise a system of equations to solve it. My husband's age," remarked a lady the other day, "is represented by the figures of my own age reversed. He is my senior, and…
TheVillageIdiot
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Does $x=x$ represent a valid algebraic equation?

I have an equation $x=x$. Is that a valid algebraic equation? Can $x=x$ be simplified to $1=1$? Can it be simplified down to True? Can $x=x$, $1=1$, or True be graphed on a regular $(x,y)$ plot graph? Could it be graphed at all? If it is graph-able…
savvamadar
  • 159
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Solve the inequality $x^4-3x^2+5\ge0$

Solve $$\sqrt{x^4-3x^2+5}+\sqrt{x^4-3x^2+12}=7.$$ $D_x:\begin{cases}x^4-3x^2+5\ge0 \\x^4-3x^2+12\ge0\end{cases}.$ We can see that $x^4-3x^2+12=(x^4-3x^2+5)+7,$ so if $x^4-3x^2+5$ is non-negative, $x^4-3x^2+12$ is also non-negative (even positive).…
Math Student
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Distance between point and a line - problems simplifying the minimised distance equation

Someone asked how to prove the distance between a point $(x_1,y_1)$ and a line $Ax + By + C = 0$ is:$$\text{Distance} = \frac{\left | Ax_{1} + By_{1} + C\right |}{\sqrt{A^2 + B^2} }$$ The currently accepted answer shows that a point on the line can…
PeteUK
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How to calculate the "difference between $X$ and $Y$"

I feel like this is the silliest question ever, so I apologize in advance! a statement reads: $Z$ is the difference between $X$ and $Y$. Which of these is true? $Z = X - Y$ $Z = Y - X$ $Z = |X - Y|$ I want to say it's the third, or whichever is…
Jacob Raccuia
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Is $\frac{1}{x} = 4$ strictly a linear equation (in one variable)?

$$\frac1{x} = 4$$ If multiplied by $x$ both sides, $$1 = 4x$$ Then it looks like linear equation in one variable. But is such multiplication by variable on both sides allowed?
Ispring Quiz
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Square root inequality $\sqrt {x-z} \geq \sqrt x -\sqrt{z} $

Does the following inequality hold? $$\sqrt {x-z} \geq \sqrt x -\sqrt{z} \ , $$ for all $x \geq z \geq 0$. My justification \begin{equation} z \leq x \Rightarrow \\ \sqrt z \leq \sqrt {x} \Rightarrow \\ 2\sqrt z \sqrt z \leq 2\sqrt z\sqrt {x}…
Math_Mania
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A fast solution of $\frac{\left|x^2-1\right|-3}{1-2x}<\:x$

If I have this easy inequality $$\frac{|x^2-1|-3}{1-2x}<\:x$$ your solutions, step by steps are $]-1,\frac{1}{2}[\,\cup\, ]\frac{4}{3},+\infty[$, considering the signs of $|x^2-1|$, i.e. $x^2-1\geq 0 \iff x\leq 1 \vee x\geq 1$ and $x^2-1<0 \iff…
Sebastiano
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On the equation $\left( x^2+100 \right)^2 = \left( x^3 -100 \right)^3$

Solve the equation $$\left( x^2+100 \right)^2 = \left( x^3 -100 \right)^3$$ I have no idea what to do. The equation is part of an exercise that goes as follows: Let $f:\mathbb{R} \rightarrow \mathbb{R}$ be a function such that $$f(f(x)) = x \quad…
Tolaso
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How do I get the factors of this?

"In the complete factorization of $y^2 - 4 - x^2 + 4x$, one of it's factors is" A) $x - 4$ B) $y + 2$ C) $y - x - 2$ D) $y - x + 2$ I did a little calculator trick I always use. I got it wrong. I've decided to study more deeply the steps required to…
Saturn
  • 7,191
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Clarification of algebraic "fallacies" - Methods of Mathematics by Richard Hamming

I am reading the book "Methods of Mathematics" by Richard Hamming. In one section he talks about certain fallacies in algebra to avoid. He gives a very clear example of accidentally dividing by zero, but then follows it with another example which he…
Aaron
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Does $-6(x-\frac{1}{2})^2$ = $-\frac{3}{2}(2x-1)^2$?

I'm confused about a question I posted this morning. I am trying to understand if $-6(x-\frac{1}{2})^2$ can be rewritten as $-\frac{3}{2}(2x-1)^2$? I tried multiplying out the expression $-6(x-\frac{1}{2})^2$ to a polynomial form $36x^2-36x+9$ but…
Doug Fir
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Prove this inequality $a \sqrt{1-b^2}+b\sqrt{1-a^2}\le1 $

Prove that for $a,b\in [-1,1]$: $$a\sqrt{1-b^2}+b\sqrt{1-a^2}\leq 1$$
Veritas
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