Solving Multi-Step Equations

Senin, 20 Maret 2023

Equations that have more than one operation require more than one step to solve. To solve this type of problem, the best strategy is to undo each operation in reverse order. In other words, work backward.

 

Example

 

 

Example

Technology Link

 

3.  Trains that float on magnets above rails have been developed in Japan. They are designed to run at a maximum speed of 341 miles per hour. This is 71 miles per hour faster than twice the speed of Japan’s bullet trains. Find the speed of the bullet trains in Japan and graph the solution.

 

Alternative Solutions : 

 

Explore             You know that the speed of the floating trains is 341 mph.

This is 71 mph faster than twice Japan’s bullet trains.

 

Plan                   Let x represent the speed of the bullet trains. Then

Translate the given information into an equation and solve.

 

Solve

 

341 = 71 + 2x                          Original equation

341 – 71 = 71 + 2x – 71          Subtract 71 from each side.

270 = 2x                                  Simplify.

                    Divide each side by 2.

135 = x                                    Simplify.

 

The bullet trains in Japan travel at 135 miles per hour.

 

Examine           Check by substituting 135 into the original equation.

341 = 71 + 2x                Original equation

341 ≟ 71 + 2(135)         Replace x with 135.

341 ≟ 71 + 270              Multiply 2 and 135.

341 = 341   ü                Add 71 and 270.

 

Consecutive integers are integers in counting order, such as 3, 4, and 5. Beginning with an even integer and counting by two will result in consecutive even integers. For example, –6, –4, –2, 0, and 2 are consecutive even integers. Beginning with an odd integer and counting by two will result in consecutive odd integers. For example, –1, 1, 3, and 5 are consecutive odd integers.

Example

Number Theory Link

 

4.   Find three consecutive even integers whose sum is 18.

 

 Alternative Solutions :

 

Explore             You know that the sum of three consecutive even

integers is –18. You need to find the three numbers.

 

Plan                  Let n represent the first even integer. Then n + 2

represents the second even integer, and n  4 represents

the third. Why?

 

Solve                 n + (n + 2) + (n + 4) = –18      Write an equation.

3n + 6 = –18                            Add like terms.

3n + 6 – 6 = –18 – 6                Subtract 6 from each side.

3n = –24                                  Simplify.

                     Divide each side by 3.

n = –8                                      Simplify.

n = –8         n + 2 = –8 – 2      n + 4 = –8 + 4

  = –6                      = –4

 

The numbers are –8, –6, and –4.

 

Examine           Check by adding the three numbers.

–8 + (–6) + (–4) ≟ –18

–18 = –18   ü.

 

 

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Labels: Mathematician

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