Solve: (a) 2t = 80 (b) -6.02 = -8.6t. We will use a property of equality to isolate the variable on one side of the equation. 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. (a) To isolatet on the left side, we use the division property of equality. We can undo the multiplication by 2 by dividing both sides of the equation by 2. 2t = 80 This is the equation to solve. 2t 80 Use the division property of equality: Divide both sides by 2. it = Simplify 4 by removing the common factor of 2 in the numerator and denominator: = 1. %3D t = 40 The product of 1 and any number is that number: 1t = t. 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}. (b) To isolatet on the right side, we use the division property of equality. We can undo the multiplication by -8.6 by dividing both sides by -8.6. -6.02 = -8.6t This is the equation to solve. -6.02 -8.6t Use the division property of equality: Divide both sides by -8.6. %3D -8.6 = t Do the division: 8.6 6.02. The quotient of two negative numbers is positive. The solution is 0.7. Verify that this is correct by checking. Solve. (a) X = 17x = 204 (b) 9.24 = -0.4r r =

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Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.