5(7b+8)=-38-4b Justify each step and list all the properties of equality.

Answer 1

You can answer this by expanding the multiplication on the left, gathering the b's on the laft-hand side of the equation, and then dividing to get an equation of the form b=n, where n is a calculated value.

The explanation/justification for each step will basically say that you can add/subtract/mutliply/divide the same quantity from both sides of the equation and the result will still be correct. For example, the first few steps might be:

5(7b+8) = 38-4b

35b + 40 = 38 - 4b [Distributive property]

35b + 4b + 40 = 38 - 4b + 4b [Added 4b to each side of the equation]

39b + 40 = 38 [Added like quantities]

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You can find a list of the properties of equality with a Google search, or they should be listed in your textbook.

Answer 2

Solution:

5(7b+8)=-38-4b First you need to isolate b

To do that you need to expand the factored side a( b + c) = ab + cd, Distributive property

5( 7b + 8) = 5(7b) + 5(8) , 35 b + 40 = -38 - 4b so add +4b to both sides of the equation

35b + 40 + 4b = -38 -4b +4b , 39b +40 = -38 now add -40 to both sides of the equation

39b + 40 -40 = -38-40, 39b = -78 , divide both sides by 39

39b/39 = -78/39 , and b = -78/39 and simplify, b = -78/39 = -2

Check by substitution of b = -2 into original equation

5(7b+8)=-38-4b , 5 [7(-2)+8] = -38 - 4(-2), 5(-14+8) = -38 + 8, -70 +40 = -38 + 8, and -30 = -30 Checks

Most common properties are commutative a + b = b + a, or ab = ba

Associative a + ( b + c) = ( a + b) + c

Distributive a( b + c) = ab + ac

Other properties are listed in your algebra text book