Solve. Type an integer or simplified fraction for: -7x -22 = -26 2/3
7x=-26 2/3 + 22
Then divide that fraction by 7.
To solve the equation -7x - 22 = -26 2/3, you need to isolate the variable x. Here's how you can do it step by step:
Step 1: Move the constant term to the other side of the equation.
-7x - 22 + 22 = -26 2/3 + 22
-7x = -26 2/3 + 22
Step 2: Add the whole numbers and fractions separately.
-26 2/3 + 22 = -26 + 2/3 + 22
To add these two fractions, they need to have a common denominator.
-26 + 22 = -4
So, the equation becomes:
-7x = -4 + 2/3
Step 3: Convert the mixed number to an improper fraction.
-4 + 2/3 = -4 + 2/3 * 3/3
= -4 + 6/3
Step 4: Add the fractions.
-4 + 6/3 = -4 + 6/3
Step 5: Simplify the fraction.
6/3 = 2
Therefore, the equation becomes:
-7x = -4 + 2
Step 6: Add the numbers on the right side of the equation.
-4 + 2 = -2
The equation now reads:
-7x = -2
Step 7: Solve for x by dividing both sides of the equation by -7.
(-7x)/(-7) = (-2)/(-7)
x = 2/7
Hence, the solution to the equation is x = 2/7.