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3 years ago

Solve for x: 17x - 12 = 114 + 3x Thanks!

Mathematics

2 answers:

wel3 years ago

7 0

Answer:

x = 9

Step-by-step explanation:

Simplifying

17x + -12 = 114 + 3x

Reorder the terms:

-12 + 17x = 114 + 3x

Solving

-12 + 17x = 114 + 3x

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-3x' to each side of the equation.

-12 + 17x + -3x = 114 + 3x + -3x

Combine like terms: 17x + -3x = 14x

-12 + 14x = 114 + 3x + -3x

Combine like terms: 3x + -3x = 0

-12 + 14x = 114 + 0

-12 + 14x = 114

Add '12' to each side of the equation.

-12 + 12 + 14x = 114 + 12

Combine like terms: -12 + 12 = 0

0 + 14x = 114 + 12

14x = 114 + 12

Combine like terms: 114 + 12 = 126

14x = 126

Divide each side by '14'.

x = 9

Simplifying

x = 9

valentinak56 [21]3 years ago

7 0

Answer:

X = 9

Step-by-step explanation:

17x - 12 = 114 + 3x

- 3 -3

14x - 12 = 114

+12 +12

14x = 126

/14 /14

x = 9

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1) Use letters to identify the variables:

Number of trumpets: t
Number of clarinets: c

2) Translate each statement into algebraic (mathematical) language.

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=> t + c = 27

2.2) Trumpets cost $149 and clarinets cost $99

Total cost of the trumpets: 149t
Total cost of clarinets: 99c

Total cost = 149t + 99c

2.3) Total sales were $3223

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3) State the system of equations:

Equation (1) t + c = 27
Equation (2) 149t + 99c = 3223

4) Solve the system of equations:

4.1) Multiply equation 1 by 149:

=> 149t + 149c = 4023

4.2) Subtract the equation (2) from the equation obtained in 4.1

=> 149c - 99c = 4023 - 3223

=> 50c = 800

=> c = 800 / 50 = 16

5) Verify the solution:

From equation (1) t = 27 - 16 = 11

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