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ASHA 777 [7]
2 years ago
5

3(x + 10) + 6 = 3(x + 12)

Mathematics
2 answers:
Talja [164]2 years ago
7 0

Answer:

infinitely many solutions / all solutions

Step-by-step explanation:

  1. you distribute    3x+30+6 = 3x+36
  2. combine like terms 3x+36 = 3x+36
  3. realise the 2 terms are the same so x can be anything
Helga [31]2 years ago
6 0

Answer:

x = infinite amount of solutions

General Formulas and Concepts:

<u>Pre-Algebra</u>

  • Order of Operations: BPEMDAS
  • Equality Properties

Step-by-step explanation:

<u>Step 1: Define equation</u>

3(x + 10) + 6 = 3(x + 12)

<u>Step 2: Solve for </u><em><u>x</u></em>

  1. Distribute 3:                              3x + 30 + 6 = 3x + 36
  2. Combine like terms:                 3x + 36 = 3x + 36
  3. Subtract 36 on both sides:      3x = 3x
  4. Divide 3 on both sides:            x = x

Here we see that <em>x</em> does indeed equal <em>x</em>. We can plug in any number <em>x</em> and it would render the equation true.

∴ x = infinite amount of solutions

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\bigstar\:{\underline{\sf{In\:right\:angled\:triangle\:ABC\::}}}\\\\

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⠀⠀⠀

\bf{\dag}\:{\underline{\frak{By\:using\:Pythagoras\: Theorem,}}}\\\\

\star\:{\underline{\boxed{\frak{\purple{(Hypotenus)^2 = (Perpendicular)^2 + (Base)^2}}}}}\\\\\\ :\implies\sf (AB)^2 = (AC)^2 + (BC)^2\\\\\\ :\implies\sf (AB)^2 = (AB)^2 = (7)^2 = (4)^2\\\\\\ :\implies\sf (AB)^2 = 49 + 16\\\\\\ :\implies\sf (AB)^2 = 65\\\\\\ :\implies{\underline{\boxed{\pmb{\frak{AB = \sqrt{65}}}}}}\:\bigstar\\\\

⠀⠀⠀⠀━━━━━━━━━━━━━━━━━━━━━

☆ Now Let's find value of sin A, cos A and tan A,

⠀⠀⠀

  • sin A = Perpendicular/Hypotenus = \sf \dfrac{4}{\sqrt{65}} \times \dfrac{\sqrt{65}}{\sqrt{65}} = \pink{\dfrac{4 \sqrt{65}}{65}}

⠀⠀⠀

  • cos A = Base/Hypotenus = \sf \dfrac{7}{\sqrt{65}} \times \dfrac{\sqrt{65}}{\sqrt{65}} = \pink{\dfrac{7 \sqrt{65}}{65}}

⠀⠀⠀

  • tan A = Perpendicular/Base = {\sf{\pink{\dfrac{4}{7}}}}

⠀⠀⠀

\therefore\:{\underline{\sf{Hence,\: {\pmb{Option\:A)}}\:{\sf{is\:correct}}.}}}

4 0
3 years ago
3(x + 1) = -2 (x - 1) -4
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Answer:

x = -1

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combine like terms

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