Please explain how to solve the linear equation to get 20 simply, please. Thank you!

Let's solve that second equation for x

12+x = 0.80(x+20)

12+x = 0.80*x + 0.80*20

12+x = 0.80x + 16

x-0.80x = 16-12

0.2x = 4

x = 4/0.2

x = 20

So that's where the 20 comes from. It's a coincidence its the same exact value as the number of total games played so far (before the x additional games are played).

Raj and Aditi like to play chess against each other have won 12 of the 20 games so far. They decide to play more games.

How many more games will Aditi have to win to have a 70% winning record?

= 12 + x = 0.70 (20 + x)

= x = 20/3 = 6.67 or 7 games more

How many more games will Aditi have to win to have a 80% winning record?

Use the distributive property to multiply 0.8 by x+20.

12 + x = 0.80 (x + 20)

12 + x= 0.8x + 16

Subtract 0.8x from both sides.

12 + x − 0.8x = 16

Combine x and −0.8x to get 0.2x.

12 + 0.2x = 16

Subtract 12 from both sides.

0.2x = 16 − 12

Subtract 12 from 16 to get 4.

0.2x = 4

Divide both sides by 0.2.

x=  4/0.2

Expand   4/0.2 = 20 by multiplying both numerator and the denominator by 10.

x=  40 ÷ 2

Divide 40 by 2 to get 20.

x=20

answer: yes, since the line has a steeper rate of change than the exponential the y-values will be greater and they will only intersect one time.

answer: solve 5\cdot 2^x=2405⋅2  

x

=2405, dot, 2, start superscript, x, end superscript, equals, 240.

solution

to solve for xxx, we must first isolate the exponential part. to do this, divide both sides by 555 as shown below. we do not multiply the 555 and the 222 as this goes against the order of operations!

\begin{aligned} 5\cdot 2^x& =240 2^x& =48 \\ \end{aligned}  

5⋅2  

x

2  

x

​    

=240

=48

​

step-by-step explanation: