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Chapter 3: Q34. (page 133)

Solve the equation. Check your solution.

3x-7=8+6x+2

Short Answer

Expert verified

The solution for the equation 3x-7=8+6x+2 is x=-9.

Step by step solution

01

– Separate the variable and constants

Write the original equation and separate the variable and constants.

3x鈭�7=8+6x+23x鈭�7=8+6x+12Usedistributiveproperty3x鈭�6x鈭�7=20+6x鈭�6xSubtract6xfrombothsides鈭�3x鈭�7=20Simplify鈭�3x鈭�7+7=20+7Add7tobothsides鈭�3x=27Simplify

02

– Solve for x

Now, divide both sides of the equation by -3.

鈭�3x鈭�3=27鈭�3x=鈭�9

Therefore, the solution of the equation is x=-9.

03

– Check the solution 

To check the solution, write the original equation and substitute the value of x.

3x-7=8+6x+2

Now, substitute x=-9 and check the result.

3鈭�9鈭�7=8+6鈭�9+2鈭�27鈭�7=8+6鈭�7鈭�34=8鈭�42鈭�34=鈭�34

As the left-hand side is equal to right hand side, this signifies that the solution is correct.

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Most popular questions from this chapter

Amusement Parks You are trying to decide whether to pay \(120 for a season pass to an amusement park. If you buy the pass, you get an unlimited number of visits to the park and reduced parking for \)8. If you do not buy the pass, you pay \(23 admission and \)10 for parking each time you visit the park. After how many visits to the park will the cost of visiting with the season pass be less than cost of visiting without the season pass?

  1. Write a variable expression for the cost of making v visits to the park if you don鈥檛 buy a season pass.
  2. Write an inequality in terms of v showing that the cost of visiting the park with a season pass is less than the cost of visiting the park without a season pass.
  3. Solve the inequality.

The table below shows the cost of renting a moving van for one day from two companies. The daily charge and the charge per mile shown below:

  1. Calculate the miles that you have to drive before the cost of renting a van for one day from company A is less than the cost of renting a van for one day from company B. Express in inequality.
  2. Draw the graph of the inequality.
  3. Find which company is less expensive of you drive 100 miles in one day. Explain.

Write and solve an equation for the following verbal sentence: Nine more than 3 times a number is equal to 7 less than twice the number. (Lesson 3.3)

Solve the inequality. Graph and check your solution.

x+3<7

Solve the equation. Check your solution.-40-(2x+5)=-61
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