Solve: 12(x3+1)=x4−2

Question

Brighton · Accepted Answer

Step 1
A linear equation in a variable x is an equation containing the variable only with its first power. Solving an equation in x is finding the value of x that satisfies the equation.
For the given equation use the distributive property of multiplication and addition $a (b + c) = a b + a c$ . Find the least common denominator of the fractions and multiply by this least common denominator to eliminate fractions.
Step 2
Given equation is $\frac{1}{2} (\frac{x}{3} + 1) = \frac{x}{4} - 2$ Remove the fractions using information from step 1. Then move the x terms to one side and constant terms to other side.
$\frac{1}{2} (\frac{x}{3} + 1) = \frac{x}{4} - 2$
$\frac{x}{6} + \frac{1}{2} = \frac{x}{4} - 2$
$12 (\frac{x}{6} + \frac{1}{2}) = 12 (\frac{x}{4} - 2)$
$2 x + 6 = 3 x - 24$
$2 x + 6 - 2 x = 3 x - 24 - 2 x$
$6 = x - 24$
$6 + 24 = x - 24 + 2 x$
$x = 30$
Hence, solution to given equation is $x = 30$ .

Solve: \frac{1}{2}\left(\frac{x}{3}+1\right)=\frac{x}{4}-2

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