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McGraw Hill Glencoe Algebra 2, 2012

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McGraw Hill Glencoe Algebra 2, 2012 View details

3. Solving Equations

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Exercise 55 Page 23

Gather all of the variable terms on one side of the equation and all of the constant terms on the other side.

k=-4

Practice makes perfect

To solve an equation, we should first gather all of the variable terms on one side of the equation and all of the constant terms on the other side, using the Properties of Equality. In this case, we need to start by using the Distributive Property to simplify the left-hand side of the equation.

5.4(3k-12)+3.2(2k+6)=-136

Distribute 5.4

16.2k-64.8+3.2(2k+6)=-136

Distribute 3.2

16.2k-64.8+6.4k+19.2=-136

Add terms

22.6k-45.6=-136

Now we can continue to solve using the Properties of Equality.

22.6k-45.6=-136

LHS+45.6=RHS+45.6

22.6k-45.6+45.6=-136+45.6

Add terms

22.6k=-90.4

▼

.LHS /22.6.=.RHS /22.6.

.LHS /22.6.=.RHS /22.6.

22.6k/22.6=-90.4/22.6

MoveNegNumToFrac

Put minus sign in front of fraction

22.6k/22.6=-90.4/22.6

Calculate quotient

k=-4

The solution to the equation is k=-4. We can check our solution by substituting it into the original equation.

5.4(3k-12)+3.2(2k+6)=-136

k= -4

5.4(3( -4)-12)+3.2(2( -4)+6)? =-136

▼

Simplify

a(- b)=- a * b

5.4(-12-12)+3.2(-8+6) ? = -136

Add and subtract terms

5.4(-24)+3.2(-2)? =-136

a(- b)=- a * b

-129.6-6.4? =-136

Subtract term

-136=-136

Since the left-hand side is equal to the right-hand side, our solution is correct.

Subchapter links

Check Your Understanding p.22

Practice and Problem Solving p.22-24

H.O.T. Problems p.24

Standardized Test Practice p.25

Spiral Review p.25

Skills Review p.25