Question 1

Solve for $$x in $$the equation $$2x + 5 = 17. $$What is the value of $$x$$?

Accepted Answer

$$x = 6$$

Question 2

Which property is used when you subtract the same number from both sides of an equation to keep it balanced?

Accepted Answer

Subtraction Property of Equality

Question 3

A chemist mixes a solution with $$x$$ grams of salt and $$3x$$ grams of sugar. If the total mass is $$40$$ grams, what is the value of $$x$$?

Accepted Answer

$$x = 10$$

Question 4

Solve for $$y in $$the equation $$5y - 2 = 3y + 10.$$

Accepted Answer

$$y = 6$$

Question 5

A patient is prescribed a medication where the dosage in mg is given by $$d = 2w + 15$$, where $$w is $$the patient's weight in kg. If the patient weighs $$35 kg$$, what is the correct dosage?

Accepted Answer

$$d = 85 mg$$

Question 6

Which of the following is the first step to solve the equation $$4(x - 3) = 20$$?

Accepted Answer

Distribute $$4 to $$both $$x$$ and $$-3$$

Question 7

If $$3x + 2 = 2x + 7$$, what is the value of $$x$$?

Accepted Answer

$$x = 5$$

Question 8

A rectangle has a length that is $$4$$ units more than twice its width. If the perimeter is $$32$$ units, what is the width?

Accepted Answer

$$w = 4$$

Question 9

Which equation represents the scenario: 'The sum of a number and its double is $$21$$'?

Accepted Answer

$$x + 2x = 21$$

Question 10

Solve for $$x in $$the equation $$\frac{2x}{3} = 8.$$

Accepted Answer

$$x = 12$$

Question 11

A historical event lasted $$x$$ years. If twice the duration minus $$5$$ equals $$19$$, how many years did the event last?

Accepted Answer

$$x = 12$$

Question 12

Which property justifies the step from $$x + 7 = 15 to$$ $$x = 8$$?

Accepted Answer

Subtraction Property of Equality

Question 13

If $$5(x - 2) = 25$$, what is the value of $$x$$?

Accepted Answer

$$x = 7$$

Question 14

A car rental company charges a flat fee of $$\30$ plus $$\$$0.20$$ per mile driven. If the total cost is $$\50$, how many miles were driven?

Accepted Answer

$$100$$ miles

Question 15

Solve for $$x in $$the equation $$7x - 4 = 3x + 12.$$

Accepted Answer

$$x = 4$$

Question 16

A biologist observes that the number of bacteria triples every hour. If there are $$x$$ bacteria now, and $$81$$ bacteria after $$4$$ hours, what is the value of $$x$$?

Accepted Answer

$$x = 3$$

Question 17

Which equation would you use to solve the following scenario: 'A number decreased by $$7 is $$equal to twice the number increased by $$5$$'?

Accepted Answer

$$x - 7 = 2x + 5$$

Question 18

If $$4x + 3 = 19$$, what is the value of $$x$$?

Accepted Answer

$$x = 4$$

Question 19

A phone plan charges $$\25$ per month plus $$\$$0.10$$ per text message. If the bill for one month is $$\40$, how many text messages were sent?

Accepted Answer

$$150$$ messages

Question 20

Solve for $$x in $$the equation $$2(x + 5) = 18.$$

Accepted Answer

$$x = 4$$

Solving Equations: Properties and Applications

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