Answer :
Answer: [tex]x=-\frac{2}{3}[/tex]
Step-by-step explanation:
Given the following equation:
[tex]\frac{2}{3}-4x+\frac{7}{2}=-9x+\frac{5}{6}[/tex]
We need to solve for "x":
1. Move the fractions to one side of the equation and the x-terms to the other side:
[tex]-4x+9x=\frac{5}{6}-\frac{2}{3}-\frac{7}{2}[/tex]
2. Add the like terms.
To add the fractions we must find the Least Common Denominator (LCD):
[tex]6=2*3\\3=3\\2=2\\\\LCD=2*3=6[/tex]
Then:
[tex]5x=\frac{5-4-21}{6}\\\\5x=-\frac{20}{6}\\\\5x=-\frac{10}{3}[/tex]
3. Finally, divide both sides of the equation by 5:
[tex]\frac{5x}{5}=\frac{-\frac{10}{3}}{5}\\\\x=-\frac{2}{3}[/tex]
By isolating the variable, we will see that the solution is x = -2/3.
How to solve the equation?
Here we have the equation:
2/3 - 4x + 7/2 = -9x + 5/6
And we want to solve this for x. To do this, we need to move all the terms with x to the left side and all the terms without x to the right side, we will get:
-4x + 9x = 5/6 - 2/3 - 7/2
Now we simplify both sides:
(-4 + 9)*x = 5/6 - 4/6 - 21/6
5x = -20/6
Now we divide both sides by 5:
x = (-20/6)*(1/5) = -4/6
x = -4/6 = -2/3
So the solution of the equation is x = -2/3.
If you want to learn more about linear equations, you can read:
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