Five times the difference of a number and two is seven more than that number

1 answer:

3 0

Answer: The number is: 4 ¼ ; or, write as 4.25 .
<span>_____________________________________________
</span>Explanation:
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We set up the problem as:
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5(x − 2) = 7+ x ; Solve for "x" (our "unknown number"; which is the answer).
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Using the "distributive property of multiplication" :
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a*(b + c) = ab + ac ; AND:

a* (b − c) = ab − ac ;
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Let us take the "left-hand side" of our equation and expand it:
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5(x − 2) = (5*x) − (5*2) = 5x − 10 ;
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and rewrite the equation; substitute our "expanded value" for the "left-hand side";
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→ 5(x − 2) = 7+ x ; ↔ 5x − 10 = 7+ x ;
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Now, subtract "x" from EACH SIDE of the equation; & add "10" to EACH SIDE of the equation;
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→ 5x − 10 − x + 10 = 7+ x − x + 10 ;
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→ to get: 4x = 17 ;
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→ Now, divide EACH side of the equation by "4"; to isolate "x" on one side of the equation; and to solve for "x" (our answer);
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→ 4x / 4 = 17 / 4;
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→ x = 17/4 = 17 ÷ 4 = 4 ¼ ; or, write as 4.25 .
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→ Answer: The number is: 4 ¼ ; or, write as 4.25 .
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→Let us check our answer:
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"Five times the difference of a number and 2" ;
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→ 5* (x − 2) = 5 * (4.25 − 2) = 5 * (2.25) = 11.25 ;

→ Is "11.25" , SEVEN MORE THAN 4.25??
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→ 11.25 − 4.25 =?? 7 ??? Yes!
__________________________________________

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