Problem 1 Simplifying Expressions

What is the simplified form of each expression?

1. 3(x + 8)

   3 ( x + 8 ) = 3 ( x ) + 3 ( 8 ) Distributive Property   = 3 x + 24 Simplify. table with 2 rows and 3 columns , row1 column 1 , 3 open x plus 8 close , column 2 equals 3 open x close plus 3 open 8 close , column 3 cap distributive cap property , row2 column 1 , , column 2 equals 3 x plus 24 , column 3 cap simplify. , end table

2. ( 5 b − 4 ) ( − 7 ) open 5 bold italic b minus 4 close open negative 7 close

   ( 5 b − 4 ) ( − 7 ) = 5 b ( − 7 ) − 4 ( − 7 )   = − 35 b + 28 table with 2 rows and 2 columns , row1 column 1 , open 5 b minus 4 close open negative 7 close , column 2 equals 5 b open negative 7 close minus 4 open negative 7 close , row2 column 1 , , column 2 equals negative 35 b plus 28 , end table

✓ Got It?

1. What is the simplified form of each expression?
   1. 5(x + 7)
   2. 12 ( 3 − 1 6 t ) 12 . open . 3 minus , 1 sixth , t . close
   3. (0.4 + 1.1c)3
   4. ( 2 y − 1 ) ( − y ) open 2 y minus 1 close open negative y close

Problem 2 Rewriting Fraction Expressions

What sum or difference is equivalent to 7 x + 2 5 ? fraction 7 x plus 2 , over 5 end fraction . question mark

7 x + 2 5 = 1 5 ( 7 x + 2 ) Write division as multiplication .   = 1 5 ( 7 x ) + 1 5 ( 2 ) Distributive Property   = 7 5 x + 2 5 Simplify . table with 3 rows and 3 columns , row1 column 1 , fraction 7 x plus 2 , over 5 end fraction , column 2 equals , 1 fifth . open , 7 x plus 2 , close , column 3 cap writedivisionasmultiplication . . , row2 column 1 , , column 2 equals , 1 fifth . open , 7 x , close . plus , 1 fifth . open 2 close , column 3 cap distributivecap property , row3 column 1 , , column 2 equals , 7 fifths , x plus , 2 fifths , column 3 cap simplify , . , end table

✓ Got It?

2. What sum or difference is equivalent to each expression?
   1. 4 x − 16 3 fraction 4 x minus 16 , over 3 end fraction
   2. 11 + 3 x 6 fraction 11 plus 3 x , over 6 end fraction
   3. 15 + 6 x 12 fraction 15 plus 6 x , over 12 end fraction
   4. 4 − 2 x 8 fraction 4 minus 2 x , over 8 end fraction

Problem 3 Using the Multiplication Property of − 1 negative 1

Multiple Choice What is the simplified form of − ( 2 y − 3 x ) ? negative open 2 bold italic y minus 3 bold italic x close question mark

1. 2y + 3x
2. − 2 y + ( − 3 x ) negative 2 y plus open negative 3 x close
3. − 2 y + 3 x negative 2 y plus 3 x
4. 2 y − 3 x 2 y minus 3 x

− ( 2 y − 3 x ) = − 1 ( 2 y − 3 x ) Multiplication Property of  − 1   = ( − 1 ) ( 2 y ) + ( − 1 ) ( − 3 x ) Distributive Property   = − 2 y + 3 x Simplify. table with 3 rows and 3 columns , row1 column 1 , negative open 2 y minus 3 x close , column 2 equals negative 1 open 2 y minus 3 x close , column 3 cap multiplication cap property of . minus 1 , row2 column 1 , , column 2 equals open negative 1 close open 2 y close plus open negative 1 close open negative 3 x close , column 3 cap distributive cap property , row3 column 1 , , column 2 equals negative 2 y plus 3 x , column 3 cap simplify. , end table

The correct choice is C.

✓ Got It?

3. What is the simplified form of each expression?
   1. − ( a + 5 ) negative open eh plus 5 close
   2. − ( − x + 31 ) negative open negative x plus 31 close
   3. − ( 4 x − 12 ) negative open 4 x minus 12 close
   4. − ( 6 m − 9 n ) negative open 6 m minus 9 n close