7.6.8 Factoring and Expanding

Rewrite the following expression in simplified, expanded form.

Rewrite the following expression in factored form.

Rewrite the following expression in expanded form.

Using the following tape diagram, solve for x.

Mathematical Equivalence

ON

Answer explanation

2(x+4)=50

Divide by 2.

x+4 = 25

Subtract 4 from both sides.

x = 21

2(x+4)=50

Distribute the 2 to (x+4)

2x+8=50

Subtract 8 from both sides.

2x = 42

Divide both sides by 2.

x=21

• Divide by 5 to each side.

• Add 1 to each side.

• Distribute the 5 to both the x and -1.

• Subtract 1 to both sides.

Mathematical Equivalence

ON

Answer explanation

2(x-3)=14

Divide both sides by 2.

x-3 = 7

Add 3 to both sides.

x=10.

2(x-3)=14

Distribute the 2 to (x-3)

2x-6=14

Add 6 to both sides.

2x=20

Divide both sides by 2.

x=10

Mathematical Equivalence

ON

Answer explanation

-5(x-1)=40

Divide both sides by -5.

x-1=-8

Add 1 to both sides.

x=-7

-5(x-1) = 40

Distribute the -5 to (x-1).

-5x+5=40

Subtract 5 from both sides.

-5x=35

Divide by -5.

x=-7

Mathematical Equivalence

ON

Answer explanation

10x+2=24

Subtract 2 from both sides.

10x=22

Divide both sides by 10.

x = 2.2

Mathematical Equivalence

ON

Answer explanation

1/6(x+10)=11

Multiply both sides by reciprocal of the fraction (6) to get rid of the fraction.

x+10=66

Subtract 10 from both sides.

x=56