Algebraic Expressions

Algebraic Expressions (Review)

We will recap how to evaluate an expression, simplify an expression, and translate an expression.

To Evaluate an Expression

When evaluating an expression, substitute any given values of the variables into an expression. Then, simplify with the order of operations.

Multiple Choice

Evaluate the following expression:

x² - x + 5 when x = 5

• 25

• 33

• 20

• 35

Multiple Choice

If g = 3 and h = 9, evaluate the following expression:

4h + 2g + 4

• 42

• 46

• 34

• 58

Multiple Choice

Evaluate m² + 12q if m = 5 and q = -3.

• 10

• -25

• -11

• 13

Simplifying Expressions

1. Distribute

 $\ \ \ \ \ \ a\left(x\pm y\right)=ax\pm by$  
2. Combine Like Terms
       Terms with the same variable(s) 
       raised to the same power(s)

Multiple Choice

Simplify: -2(n + 5) + 3n

• n + 10

• n - 10

• 5n + 5

• 5n - 5

Multiple Choice

Simplify the expression:

-4x +6(x + 2)

• -10x + 12

• -10x + 8

• 2x + 12

• 2x+8

Multiple Choice

Simplify the following expression:

3(2x - 5) + 5x - 4

• 11x - 19

• 11x - 11

• 6x + 11

• 6x + 19

Translating Expressions

• For "more than", "less than" and "subtracted from", reverse the order of the terms in the expression

• Squared = 2nd power

• Cubed = 3rd Power

• For word problems, remember that phrases such as "for each", "for every", and "per" usually mean multiplication.

Multiple Choice

Which algebraic expression represents "six less than a number"?

• 6/k

• k/6

• 6 - k

• k - 6

Multiple Choice

Translate the following into an algebraic expression:

Ten decreased by four times a number.

• 10 - 4x

• 4x - 10

• 10 - x

• 10/4x

Multiple Choice

Translate this phrase into an algebraic expression:

8 less than the product of 4 and a number.

• 4m + 8

• 8m - 4

• 8m + 4

• 4m - 8

Multiple Choice

Translate this phrase into an algebraic expression:

2 times the sum of t and 11

• 2t + 11

• 2(t + 11)

• 2(t / 11)

• 2t - 11

Multiple Choice

Luke's parents hired a magician for his birthday party. The magician charges $100 plus an additional $20 per hour. If h represents the hours, which expression represents how much Luke's parents spent on the magician?

• $100\ +\ 20h$

• $100h\ +\ 20$

• $100\ +\frac{h}{20}$

• $100\ +\ h$

Multiple Choice

Aaron went to Game Stop to purchase a used games. They had a special promotion where, for a limited time, all used games were half price. He also had a coupon for $10 off of his total purchase. If g represents the full regular cost of the games Aaron purchased, which expression represents the price he pays before taxes?

•  $\frac{g}{2}\ -\ 10$ 

•  $\frac{g}{2}+10$ 

•  $2g\ -\ 10$ 

•  $\frac{g}{10}-2$