Question

18. Find the value of x that makes the equation true.

Answer 1

Step-by-step explanation:

✧ $\large{ \tt{ \: \frac{1}{2} x + 2 = \frac{3}{2} x - 6}}$

We need to get rid of the fractions. Notice that there are 4 terms in the equation. Multiply both sides of the equation by 2 to get rid of the fractions. Multiply by 2 because 2 is the denominator.

⤑ $\large{ \tt{2( \frac{1}{2} x + 2) = 2( \frac{3}{2} x - 6)}}$

⤑ $\large{ \tt{x + 4 = 3x - 12}}$

Subtract 4 from both sides in order to isolate the variable on the left.

⤑ $\large{ \tt{x + 4 - 4 = 3x - 12 - 4}}$

⤑$\large{ \tt{x = 3x - 16}}$

Move 3x to left hand side and change it's sign

⤑$\large {\tt{x - 3x = - 16}}$

Subtract 3x from 1x

⤑ $\large{ \tt{ - 2x = - 16}}$

Divide both sides of the equation by -2

⤑ $\large{ \tt{ \frac{ - 2x}{ - 2} = \frac{ - 16}{ - 2}}}$

⤑ $\large{ \tt{x = 8}}$

$\boxed{ \boxed{ \underline{ \tt{Our \: Final \: Answer : \boxed{ \underline{ \tt{x = 8}}}}}}}$

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