EXAMPLE 7 Solve: (a) 2t=80 (b) -6.02-8.6t
Strategy
Why
We will use a property of equality to isolate the variable on one side of the
equation.
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To solve the original equation, we want to find a simpler equivalent equation of the
form t= a number or a number = t, whose solution is obvious.
Solution (a) To isolate t on the left-hand side, we can undo the multiplication by 2 by dividing both sides by 2.
2t = 80
This is the equation to solve.
Use the division property of equality: Divide both sides by 2.
2t
2
Self Check 7 Solve:
=
Read It
Simplify (21)/2 by removing the common factor of 2 in the numerator and denominator: 2/2 = 1.
The product of 1 and any number is that number: 1t = t.
t = 40
If we substitute 40 for t in 2t = 80, we obtain the true statement 80 = 80. This verifies that 40 is the solution. The solution set is (40).
1t=
(b) To isolate t on the right side, we use the division property of equality. We can undo the multiplication -8.6 by dividing both sides by -8.6.
This is the equation to solve.
-6.02-8.6t
Use the division property of equality: Divide both sides by -8.6.
Do the division: 8.6)6.02. The quotient of two negative numbers is positive.
80
-6.02 -8.6t
-8.6
The solution is 0.7. Verify that this is correct by checking.
W
(a) 18x=234
X=
Watch It
(b) 15.66= -0.6r
r=
