t = 4
Step-by-step explanation:
Solve for t:
8 - (7 t)/10 = 6 - t/5
Hint: | Put the fractions in 8 - (7 t)/10 over a common denominator.
Put each term in 8 - (7 t)/10 over the common denominator 10: 8 - (7 t)/10 = 80/10 - (7 t)/10:
80/10 - (7 t)/10 = 6 - t/5
Hint: | Combine 80/10 - (7 t)/10 into a single fraction.
80/10 - (7 t)/10 = (80 - 7 t)/10:
1/10 (80 - 7 t) = 6 - t/5
Hint: | Put the fractions in 6 - t/5 over a common denominator.
Put each term in 6 - t/5 over the common denominator 5: 6 - t/5 = 30/5 - t/5:
(80 - 7 t)/10 = 30/5 - t/5
Hint: | Combine 30/5 - t/5 into a single fraction.
30/5 - t/5 = (30 - t)/5:
(80 - 7 t)/10 = (30 - t)/5
Hint: | Make (80 - 7 t)/10 = (30 - t)/5 simpler by multiplying both sides by a constant.
Multiply both sides by 10:
(10 (80 - 7 t))/10 = (10 (30 - t))/5
Hint: | Cancel common terms in the numerator and denominator of (10 (80 - 7 t))/10.
(10 (80 - 7 t))/10 = 10/10×(80 - 7 t) = 80 - 7 t:
80 - 7 t = (10 (30 - t))/5
Hint: | In (10 (30 - t))/5, divide 10 in the numerator by 5 in the denominator.
10/5 = (5×2)/5 = 2:
80 - 7 t = 2 (30 - t)
Hint: | Write the linear polynomial on the left hand side in standard form.
Expand out terms of the right hand side:
80 - 7 t = 60 - 2 t
Hint: | Move terms with t to the left hand side.
Add 2 t to both sides:
2 t - 7 t + 80 = (2 t - 2 t) + 60
Hint: | Look for the difference of two identical terms.
2 t - 2 t = 0:
2 t - 7 t + 80 = 60
Hint: | Group like terms in 2 t - 7 t + 80.
Grouping like terms, 2 t - 7 t + 80 = 80 + (2 t - 7 t):
80 + (2 t - 7 t) = 60
Hint: | Combine like terms in 2 t - 7 t.
2 t - 7 t = -5 t:
-5 t + 80 = 60
Hint: | Isolate terms with t to the left hand side.
Subtract 80 from both sides:
(80 - 80) - 5 t = 60 - 80
Hint: | Look for the difference of two identical terms.
80 - 80 = 0:
-5 t = 60 - 80
Hint: | Evaluate 60 - 80.
60 - 80 = -20:
-5 t = -20
Hint: | Divide both sides by a constant to simplify the equation.
Divide both sides of -5 t = -20 by -5:
(-5 t)/(-5) = (-20)/(-5)
Hint: | Any nonzero number divided by itself is one.
(-5)/(-5) = 1:
t = (-20)/(-5)
Hint: | Reduce (-20)/(-5) to lowest terms. Start by finding the GCD of -20 and -5.
The gcd of -20 and -5 is -5, so (-20)/(-5) = (-5×4)/(-5×1) = (-5)/(-5)×4 = 4:
t = 4
