Intereting Posts

Congruence Relation with exponents and variables
Efficient computation of the trajectory of roots of a parameterized polynomial
Counterexample for the stability of orthogonal projections
Prove that the polynomial $f_n(x)=nx^{n+1}-(n+1)x^n+1$ is divisible by $(x-1)^2$
identify the topological type obtained by gluing sides of the hexagon
$\mathrm{rank}(A)+\mathrm{rank}(I-A)=n$ for $A$ idempotent matrix
Find the period of $\cos x -\sin x$
If $H$ is a cyclic subgroup of $G$ and $H$ is normal in $G$, then every subgoup of $H$ is normal in $G$.
How do you integrate $e^{x^2}$?
How do you make less mistakes in math?
What is the single most influential book every mathematician should read?
Prove that the following set is dense
Limit of $a_{k+1}=\dfrac{a_k+b_k}{2}$, $b_{k+1}=\sqrt{a_kb_k}$?
Non-associative, non-commutative binary operation with a identity
Unions and intersections: $(A \cup B = A ∪ C) \land (A \cap B = A ∩ C) \implies B = C.$

$y = 4y + 9$

How do I isolate y?

Can I do

- Trig sum: $\tan ^21^\circ+\tan ^22^\circ+…+\tan^2 89^\circ = ?$
- Injective functions also surjective?
- How do you factor a quadratic expression, without using the formula?
- Help solving a limit in two parts $\lim_{t\to 0}\left(\frac{1}{t\sqrt{1+t}}-\frac{1}{t}\right)$
- How find the value of the $x+y$
- Percentage to absolute value within another range?

$y = 4y + 9$

$\frac{y}{4y} = 9$ etc

Also some other questions please:

- $\frac{5x + 1}{3} – 4 = 5 – 7x$

In the above (1), if I want to remove the ‘3’ from the denominator of the LHS, do I multiply **everything** on the RHS by 3? What about the ‘-4’ on the LHS, do I do anything to that?

- In the above

$\frac{y}{4y}$

If I want to solve it, do I cross a y out from the top, or from the bottom? Does that make sense ? :\

Thanks in advance..I have an exam tomorrow..

- Question about generating function in an article
- What is the solution to the equation $9^x - 6^x - 2\cdot 4^x = 0 $?
- Manipulating Algebraic Expression
- How to calculate the percentage of increase/decrease with negative numbers?
- Explanation of method for showing that $\frac{0}{0}$ is undefined
- Proving the AM-GM inequality for 2 numbers $\sqrt{xy}\le\frac{x+y}2$
- prove that $\tan(\alpha+\beta) = 2ac/(a^2-c^2)$
- Number of solutions of Frobenius equation
- Why does $\sqrt{x^2}=|x|$?
- How to prove that the set $A = \left\{ {p:{p^2} < 2,p \in {\Bbb Q^+}} \right\}$ has no greatest element?

To make $y$ the subject or isolate $y$ try to think of equations as ‘weighing scales’ you can carry out any operation you like but you must do the same to both sides (to keep it balanced):

$$y = 4y + 9$$

$$\implies y-4y=9+4y-4y\tag{1}$$

$$\implies-3y=9$$

$$\implies \frac{-3y}{-3}=\frac{9}{-3}\tag{2}$$

$$\implies y =-3$$

For $(1)$ I subtracted $4y$ from *both sides*.

For $(2)$ I divided *both sides* by $-3$.

To move on

$$\cfrac{5x+1}{3}-4=5-7x$$

$$\implies \cfrac{5x+1}{3}=9-7x$$

$$\implies 5x+1=3\times(9-7x)$$

$$\implies 5x+1=27-21x$$

$$\implies 26x+1=27$$

$$\implies 26x=27-1$$

$$\implies 26x=26$$

$$\implies x=1$$

Others have already given you the answer, so I won’t reiterate.

Instead let me point out to you how you should think about such questions.

It appears to me that you have no firm grasp of what equations are and how to manipulate them. This is not a shame, it’s not easy to learn and also not easy to teach.

You’re approaching the problem with the mindset “here is the equation, what technique do I need to use?”. People trained in mathematics use techniques without thinking much about them, because it has become second nature. However, when you learn about the techniques you should never try to blindly apply techniques without understanding. At best, this leads to a lot of mental overhead because you have to memorize seemingly “random” facts. At worst, it leads to general confusion and to you applying methods when they seem to work but actually don’t.

Think of the equation as a scale. Everything you do to one side, you also want to do to the other side. If you compute $\frac{y}{4y}$, you effectively divide the left hand side by $4y$. But does that match up what you’re doing to the right hand side? Assuming you have a firm grasp of how to manipulate fractions, you should see that this is not the case.

I hope this helps and doesn’t come across as too condescending, I could be judging your level of knowledge wrong.

You have the right idea to get $y$ by itself on the left. However, instead of dividing by $4y$, you would subtract $4y$ from both sides. This will give you

$$y – 4y = 9.$$

Now, if you combine the like $y$-terms on the left. What would $y – 4y$ turn into? You can think of this as: $1y – 4y$.

For your next problem, if you want to multiply both sides by $3$, then you multiply **everything** by $3$, including the $-4$ on the left-hand side.

- What's the “limit” in the definition of Riemann integrals?
- Does the series $\;\sum\limits_{n=0}^{\infty}\left(\frac{\pi}{2} – \arctan(n)\right)$ converge or diverge?
- Cardinality of the set of bijective functions on $\mathbb{N}$?
- Area under parabola using geometry
- Eisenstein Criterion with a twist
- $f$ strictly increasing does not imply $f'>0$
- Proving limit with $\log(n!)$
- Prove: Square Matrix Can Be Written As A Sum Of A Symmetric And Skew-Symmetric Matrices
- Analysis Constructing a Sequence
- Integral of exponential using error function
- Determine the matrix relative to a given basis
- $U^*\otimes V$ versus $L(U,V)$ for infinite dimensional spaces
- How to maximize the number of operations in process
- Algorithm for calculating $A^n$ with as few multiplications as possible
- Let $f:R\rightarrow S$ be a ring homomorphism. Prove or disprove: if $f$ is onto and $R$ is an integral domain, then $S$ is an integral domain