What is the solution of the equation 5/3−2x=1/6?(1 point)
Responses
−11/3
negative Start Fraction 11 over 3 End Fraction
3/4
Start Fraction 3 over 4 End Fraction
3
3
−11/12
The solution to the equation 5/3 − 2x = 1/6 is -11/12.
To solve the equation 5/3 - 2x = 1/6, we need to isolate the variable x.
Step 1: Subtract 5/3 from both sides of the equation to move it to the right side:
5/3 - 5/3 - 2x = 1/6 - 5/3
-2x = 1/6 - 5/3
Step 2: Find a common denominator for 1/6 and 5/3, which is 6:
-2x = (1 * 3)/(6) - (5 * 2)/(6)
-2x = 3/6 - 10/6
Step 3: Simplify the right side by subtracting the numerators:
-2x = (3 - 10)/6
-2x = -7/6
Step 4: Divide both sides of the equation by -2 to isolate x:
(-2x) / -2 = (-7/6) / -2
x = 7/12
Therefore, the solution to the equation 5/3 - 2x = 1/6 is x = 7/12.
To solve the equation 5/3−2x=1/6, we need to isolate the variable x. Here's how you can do it:
Step 1: Start by subtracting 5/3 from both sides of the equation to get rid of the term with x on one side. This step will give us: -2x = 1/6 - 5/3.
Step 2: Now, we need to find a common denominator for 1/6 and 5/3, which is 6. Multiplying 1/6 by 2/2 gives us 2/12, and multiplying 5/3 by 2/2 gives us 10/6.
Step 3: Subtracting 10/6 from 2/12 gives us -8/6.
Step 4: Simplifying -8/6 by dividing both the numerator and denominator by 2 gives us -4/3.
Step 5: Finally, divide both sides of the equation by -2 to solve for x. This gives us x = -4/3 ÷ -2.
Step 6: To divide fractions, we multiply the first fraction by the reciprocal of the second fraction. So (-4/3) ÷ (-2) becomes (-4/3) × (-1/2).
Step 7: Simplifying this multiplication gives us (-4/3) × (-1/2) = (4/3) × (1/2) = 4/6.
Step 8: Simplifying 4/6 by dividing both the numerator and denominator by 2 gives us 2/3.
Therefore, the solution to the equation 5/3−2x=1/6 is x = 2/3.