Solve: StartFraction 2 Over 3 EndFraction minus 4 x plus StartFraction 7 Over 2 EndFraction equals negative 9 x plus StartFraction 5 Over 6. EndFraction. – 4x + = –9x +
To solve for x in the given equation:
StartFraction 2/3 EndFraction - 4x + StartFraction 7/2 EndFraction = -9x + StartFraction 5/6 EndFraction.
First, we can simplify the left side of the equation:
Convert 7/2 to have a common denominator of 6: StartFraction 7/2 EndFraction = StartFraction 7/2 * 3/3 EndFraction = StartFraction 21/6 EndFraction.
Now the equation becomes:
StartFraction 2/3 EndFraction - 4x + StartFraction 21/6 EndFraction = -9x + StartFraction 5/6 EndFraction.
Next, reduce StartFraction 2/3 EndFraction to have a common denominator of 6:
StartFraction 2/3 EndFraction = StartFraction 2/3 * 2/2 EndFraction = StartFraction 4/6 EndFraction.
Now our equation looks like:
StartFraction 4/6 EndFraction - 4x + StartFraction 21/6 EndFraction = -9x + StartFraction 5/6 EndFraction.
Combine the fractions:
StartFraction 4 + 21 EndFraction / 6 - 4x = -9x + StartFraction 5 EndFraction / 6.
StartFraction 25 EndFraction / 6 - 4x = -9x + StartFraction 5 EndFraction / 6.
StartFraction 25 EndFraction / 6 - StartFraction 24x EndFraction /6 = StartFraction -9x + 5 EndFraction / 6.
Subtract 24x from both sides:
StartFraction 25 EndFraction / 6 - StartFraction 24x EndFraction / 6 = StartFraction -9x + 5 EndFraction / 6.
StartFraction 25 - 24x EndFraction / 6 = StartFraction -9x + 5 EndFraction / 6.
Now we can equate the fractions:
25 - 24x = -9x + 5.
Move all terms involving x to one side and numerical constants to the other side:
25 - 5 = -9x + 24x.
20 = 15x.
Divide by 15 to solve for x:
x = 20 / 15.
x = 4/3.
Therefore, the solution to the equation is x = 4/3.