Question

Cfrac%7B5%7D%7B2%7D%20x" id="TexFormula1" title=" - \frac{17}{6} x + 1 = \frac{7}{6} - \frac{5}{2} x" alt=" - \frac{17}{6} x + 1 = \frac{7}{6} - \frac{5}{2} x" align="absmiddle" class="latex-formula">
can someone help me solve this?
and also explain how you got the answer too
thank you

Answer 1

$-\dfrac{17}{6}x+1=\dfrac{7}{6}-\dfrac{5}{2}x\\\\\text{Most people do not like fractions. Well, let's get rid of them.}\\\\\text{Find the common denominator.... It's 6 :)}.\\\\\text{Multiply both sides of the equation by 6:}\\\\6\!\!\!\!\diagup^1\cdot\left(-\dfrac{17}{6\!\!\!\!\diagup_1}x\right)+6\cdot1=6\!\!\!\!\diagup^1\cdot\dfrac{7}{6\!\!\!\!\diagup_1}-6\!\!\!\!\diagup^3\cdot\dfrac{5}{2\!\!\!\!\diagup_1}x\\\\-17x+6=7-3\cdot5x\qquad\text{subtract 6 from both sides}$

$-17x=1-15x\qquad\text{add 15x to both sides}\\\\-2x=1\qquad\text{divide both sides by (-2)}\\\\\boxed{x=-\dfrac{1}{2}}$