Question

Which represents the solution set of 5(x+5)<85?

A.) x<12
B.) x>12
C.) x<16
D.) x>16

Answer 1

The correct answer is: [A]: " x < 12 " .
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Given:
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" 5(x + 5) < 85 " ; Simplify/ solve for "x" ;
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Method 1)
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Note the "distributive property of multiplication" :
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a(b + c) = ab + ac ;

a(b – c) = ab – ac .
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So, take the "left-hand side" of the inequality; and expand:
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→ 5(x + 5) = (5*x) + (5*5) = 5x + 25 ;

Now, rewrite the inequality:

→ 5x + 25 < 85 ;

Subtract "25" from each side of the inequality ;

→ 5x + 25 – 25 < 85 – 25 ;

to get:
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→ 5x < 60 ;

Divide each side of the inequality by "5" ;

→ 5x / 5 < 60 / 5 ;

→ x < 12 ; which is: Answer choice: [A]: " x < 12 " .
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Method 2)
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Given:
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" 5(x + 5) < 85 " ; Simplify/ solve for "x" ;
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Divide EACH SIDE of the equation by "5" ;

[5(x + 5) ] / 5 < 85 / 5 ;

to get:

→ x + 5 < 17 ;

Subtract "5" from EACH SIDE of the inequality:

→ x + 5 – 5 < 17 – 5 ;

to get:

→ x < 12 ; which is: Answer choice: [A]: " x < 12 " .
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Answer 2

Isolate the VARIABLE by dividing each side by FACTROS that don't contain the VARIABLE .
YOUR answer is x<12