MHB Solve Inequality & Simul Eqns: Alg Workings Q (a,b,c)

  • Thread starter Thread starter Help seeker
  • Start date Start date
AI Thread Summary
To solve the inequality 5(3x + 1) < 11x, first simplify to find x, noting that multiplying or dividing by a negative changes the inequality's direction. For the simultaneous equations 3x^2 + y^2 - 7 = 0 and y - 3x - 5 = 0, substitute y with 3x + 5 into the first equation to derive a quadratic equation for x, yielding two solutions. Finally, check which of these x values also satisfy the inequality 5(x + 1) < x. The discussion emphasizes clear algebraic workings and the importance of verifying solutions against all conditions.
Help seeker
Messages
15
Reaction score
0
Q.
(a) Solve the inequality 5(3x + 1) &lt;11x, Show clear algebraic working. (2)
(b) Solve the simultaneous equations 3x 2 + y 2 – 7 = 0, y – 3x – 5 = 0 Show clear algebraic working. (4)
(c) Hence find the value of x for which 5(x + 1) &lt; x and 3x 2 + y 2 – 7 = 0 and y – 3x – 5 = 0
 
Mathematics news on Phys.org
assuming you mean ...

(a) $5(3x+1) \le 11x$

solve for $x$ as you would any other equation ...
though probably not necessary to know in this case, be aware that multiplying or dividing by a negative value changes the direction of the inequality

(b) $3x^2 + y^2 - 7 = 0$
$y - 3x - 5 = 0 \implies y = 3x+5$

I would substitute $(3x+5)$ for $y$ in the first equation and solve the resulting quadratic for $x$ ... note you'll get two ordered pairs that satisfy the system

(c) Decide which of the two (or maybe both) values for $x$ from part (b) satisfy the given inequality
 
Suppose ,instead of the usual x,y coordinate system with an I basis vector along the x -axis and a corresponding j basis vector along the y-axis we instead have a different pair of basis vectors ,call them e and f along their respective axes. I have seen that this is an important subject in maths My question is what physical applications does such a model apply to? I am asking here because I have devoted quite a lot of time in the past to understanding convectors and the dual...
Fermat's Last Theorem has long been one of the most famous mathematical problems, and is now one of the most famous theorems. It simply states that the equation $$ a^n+b^n=c^n $$ has no solutions with positive integers if ##n>2.## It was named after Pierre de Fermat (1607-1665). The problem itself stems from the book Arithmetica by Diophantus of Alexandria. It gained popularity because Fermat noted in his copy "Cubum autem in duos cubos, aut quadratoquadratum in duos quadratoquadratos, et...
Insights auto threads is broken atm, so I'm manually creating these for new Insight articles. In Dirac’s Principles of Quantum Mechanics published in 1930 he introduced a “convenient notation” he referred to as a “delta function” which he treated as a continuum analog to the discrete Kronecker delta. The Kronecker delta is simply the indexed components of the identity operator in matrix algebra Source: https://www.physicsforums.com/insights/what-exactly-is-diracs-delta-function/ by...

Similar threads

Replies
18
Views
4K
Replies
9
Views
3K
Replies
4
Views
1K
Replies
8
Views
3K
Replies
5
Views
2K
Replies
2
Views
1K
Back
Top