The equation 5/3x+11/3=−4/3 is solved as follows. Fill in the correct numbers to complete the solution.(1 point) 5/3x+11/3=−4/3 5/3x= Subtract 11/3 from both sides. x= Multiply both sides by 3/5, the reciprocal of 5/3.
To solve the equation 5/3x + 11/3 = -4/3, we need to isolate x on one side of the equation.
First, we subtract 11/3 from both sides:
5/3x + 11/3 - 11/3 = -4/3 - 11/3
5/3x = -15/3
Next, we simplify the right side:
5/3x = -5
To isolate x, we multiply both sides by the reciprocal of 5/3 (which is 3/5):
(5/3x)(3/5) = -5(3/5)
15/15x = -15/5
Simplifying further:
x = -3
So the solution to the equation is x = -3.
To solve the equation 5/3x + 11/3 = -4/3, we need to isolate the variable x by performing the necessary operations.
1. First, subtract 11/3 from both sides:
5/3x + 11/3 - 11/3 = -4/3 - 11/3
5/3x = -4/3 - 11/3
2. Combine the fractions on the right-hand side:
5/3x = (-4 - 11)/3
5/3x = -15/3
3. Next, multiply both sides of the equation by the reciprocal of 5/3, which is 3/5:
(3/5) * (5/3x) = (3/5) * (-15/3)
(3/5)*(5/3)x = -45/15
4. Simplify the left-hand side:
(3/5)*(5/3)x = (3/1)*(1/1)x
x = (3/1)x
5. Simplify the right-hand side:
-45/15 = -3
Therefore, the solution to the equation is x = -3.
To complete the solution, let's follow the steps given:
Step 1: Start with the equation: 5/3x + 11/3 = -4/3
Step 2: Subtract 11/3 from both sides:
5/3x = -4/3 - 11/3
5/3x = -15/3
Step 3: Simplify the right side:
5/3x = -5
Step 4: Multiply both sides by the reciprocal of 5/3, which is 3/5:
(3/5) * (5/3x) = (3/5) * (-5)
x = -3/5
Therefore, the solution is x = -3/5.