What is the value of x? Enter your answer in the box. x =

Mathematics

2 answers:

galina1969 [7]2 years ago

4 0

The answer is: " 11 " .
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→ " x = 11 " .
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Explanation:
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Set up the ratio/ proportion as a fraction:

6 cm / 48 cm = 5 cm / (3x + 7) ;

→ The "cm" units cancel out; since: "cm/cm = 1 " ;

→ The "6/48" = "(6 ÷ 6) / (48 ÷ 6) = " 1/8 " ;

→ Rewrite as: $\frac{1}{8} = \frac{5}{3x + 7}$ ;

Now, we can "cross-multiply" :
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<u>Note</u>: $Given: \frac{a}{b} = \frac{c}{d}$ ; $ad = bc$ ;
{b $\neq 0$ ; d $\neq 0$ } .
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As such:

1 * (3x + 7) = 8 * 5 ;

→ 3x + 7 = 40 ;

Subtract "7" from each side of the equation:

→ 3x + 7 − 7 = 40 <span>− 7 ;
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to get:

→ 3x = 33 ;

Now, divide each side of the equation by "3" ;
to isolate "x" on one side of the equation; & to solve for "x" ;

→ 3x / 3 = 33 / 3 ;

to get:
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→ " x = 11 " .
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→ The answer is: " 11 " .
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