Numerical Expressions
Write and evaluate the numerical expression for "3 squared plus 5."
Then evaluate.
Expression: 32+5
Value: 9+5=14
Translate to a numerical expression: "Seven more than x."
x+7
Identify the variable and what it could represent: 5x in the problem "it costs $5 per pack of pens at the store."
Variable: x; represents number of pens in one pack
Use the distributive property to rewrite 3(2+x) as an equivalent expression.
6+3x
Write an inequality to represent: "x is greater than 7." Then show its solution on a number line (remember dot and arrow).
Inequality: x>7.
On number line: open circle at 7, arrow shading to the right
Evaluate the expression 42+2×3 following order of operations.
22
Translate to words: 3n−5
"Three times a number n minus five."
Evaluate 7a+2 when a=3.
7(3)+2=
21+2=
23
Combine like terms to simplify: 4x+3x.
7x
Determine whether the number 5 makes the inequality x+2<8 true.
Check: 5+2<8
7<8
true
Write a numerical expression that uses a whole-number exponent to represent "the cube of 2 plus 7." Evaluate it.
23+7=
8+7=
15.
Translate to a numerical expression: "The product of 4 and the sum of 2 and y."
4(2+y)
Use substitution to determine whether x=4 makes the equation 2x+3=11 true
2(4)+3=11, so yes, true.
Apply distributive property and combine like terms to simplify: 2(3x+4)+x
2(3x+4)+x=
6x+8+x=
7x+8
Write an inequality for: "A student needs at least 60 points to pass; let p be the student's points." Represent the solution set in words.
Inequality: p≥60. Solution in words: all scores 60 or higher pass.
Evaluate 23×3+52
Show the order you used.
23×3+52=
8×3+25=
24+25=
49
Write a verbal expression for 2(3+m)−4.
"Two times the sum of 3 and m, minus 4"
Represent this real-world situation with an expression: "A movie ticket costs $8. Snacks cost $y. Write an expression for the total cost of one ticket and snacks." Then evaluate when y=5.
8+y. If y=5: 8+5=13
Show two different equivalent expressions for y+y+y and explain why they are equivalent.
Equivalent expressions: 2y+y and 3y; they are equivalent because both equal three times y for any y.
Solve and graph the inequality: x−4>3. State the solution set and show how you would draw it on a number line.
Solve: x−4>3⇒x>7
Graph: open circle at 7, shade right.
A formula gives the area of a square as A=s2. If s=6, write the numerical expression and evaluate to find A.
A=62=36.
Translate to an algebraic expression: "Twice the difference of a number n and 6, increased by 3." Then evaluate when n=10.
Expression: 2(n−6)+3.
When n=10: 2(4)+3=
8+3=
11
The expression 1/2 𝑎(𝑏+𝑐) can be used to find the area of a trapezoid. What is the area of the trapezoid when a = 6.5, b = 5, and c = 5.4?
33.8 ft2
Rewrite and simplify 6(2x+3)+4x fully by applying properties of operations.
6(2x+3)+4x=
12x+18+4x=
16x+18
A store requires that a purchase be less than $50. Write an inequality for the price p. Explain why this inequality has infinitely many solutions.
Inequality: p<50.
Infinitely many solutions because any number less than 50 (including decimals) works; examples: 49, 10, 0.