Kishore is making a 7 feet high door. If the height is 1 foot more than twice its width, what is its width?

Use inductive reasoning to make a conjecture about the sum of a number and itself. Then use deductive reasoning to show the conjecture is true.

Informally, a hypothesis is just drawing assumptions about something based on what you already know and have observed.
A conjecture is formally defined as a based-on-observations, a statement considered true.
Speculation is similar to your opinion about something you follow or perhaps a knowledgeable estimate.
For example, observe the numbers below: 2, 4, 6, 8, 10, and 12. What number would come next? You're probably thinking 14, but What led you to that conclusion, and why? You may have seen the pattern and that the list is counting in twos.
The following number is 14 because the list counts by 2's, according to your hypothesis.
You saw the pattern and concluded without making any claim.

Solve for x: 6 ( x + 1)= 4(1 +  ) + 6 + 3x

: If 𝑛 is an even integer, then 𝑚𝑛, where m is any other integer is
a. Odd
b. Even
c. Cannot be determined

When Apple sells their iPads, they increase the price $50 from what it costs them to actually make the iPads. One Apple store sold 10 iPads one day which cost a total of $5000. How much does an iPad cost to actually make?

State the law of logic that is illustrated.
If 𝑥 > 10, then 𝑥 + 10 > 20.
The value of 𝑥 is 15.
Therefore, 25 > 20.

For Christmas, Maryland purchased subscriptions to Xbox Live for her four children. Each subscription costs $5 per month plus a $15 sign-up fee. If she received a bill for $120, for how many months did she purchase subscriptions for her children?

State the law of logic that is illustrated.
If 𝑥 + 2 = 4, then 𝑥 = 2.
If 𝑥 = 2, then 𝑥²  = 4.
If 𝑥+2=4, then 𝑥² = 4

Show the conjecture is false by finding a counterexample. If A, B and C are collinear, then AB + BC = AC.

After an oil pipeline burst one morning, gas prices went up by $2.20 per gallon. If that afternoon you bought 10 gallons of gas for $53.90, what was the price per gallon before the oil pipeline burst that morning?

Show the conjecture is false by finding a counterexample. Two supplementary angles form a linear pair.

A store had homemade sweaters on sale for $20 off the original price. Aunt Ethel jumped at the bargain and bought a sweater for all 15 members of her family. If Aunt Ethel paid $375 for all the sweaters, what was the original price of each sweater?

Gym charges a $50 activation fee and $17 per month for a membership. If you spend $356, for how many months do you have a gym membership?

State the law of logic that is illustrated.
If you score more than 75%, then you can go to the beach.
If you go to the beach, then you can surf.
If you score more than 75%. Then you can surf

Show the conjecture is false by finding a counterexample. Two adjacent angles always form a linear pair.

Prove that ∠ ABC ≅ ∠ ADC