What value of x makes this equation true? 3( 1/2x+4)= 2x+2

Mathematics

1 answer:

LuckyWell [14K]3 years ago

6 0

3(1/2x +4) = 2x +2

Use distributive property by multiply 3 by each term on the left side:

3/2x + 12 = 2x + 2

Subtract 12 from both sides:

3/2x = 2x -10

Subtract 2x from both sides:

-1/2x = -10

Multiply both sides by -2:

x = 20

Answer: x = 20

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$\bf 19^{\frac{7}{4}}\cdot \sqrt[a]{19^b}=19^{\frac{5}{2}}\sqrt{19}\\\\
-----------------------------\\\\
a^{\frac{{ n}}{{ m}}} \implies \sqrt[{ m}]{a^{ n}} \qquad \qquad
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-----------------------------\\\\
thus\qquad 19^{\frac{7}{4}}\cdot 19^{\frac{b}{a}}=19^{\frac{5}{2}}\cdot 19^{\frac{1}{2}}\implies 19^{\frac{7}{4}+\frac{b}{a}}=19^{\frac{5}{2}+\frac{1}{2}}
\\\\\\
$

$\bf 19^{\frac{7}{4}+\frac{b}{a}}=19^{\frac{6}{2}}\implies 19^{\frac{7}{4}+\frac{b}{a}}=19^3\impliedby 
\begin{array}{llll}
\textit{same base, thus}\\
\textit{exponents must be the same}
\end{array}
\\\\\\
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