1.2 Use the Language of Algebra

Translate from algebra into English:

ⓐ $17 \leq 26$ ⓑ $8 \neq 17 - 3$ ⓒ $12 > 27 \div 3$ ⓓ $y + 7 < 19$

Translate from algebra into English:

ⓐ $14 \leq 27$ ⓑ $19 - 2 \neq 8$ ⓒ $12 > 4 \div 2$ ⓓ $x - 7 < 1$

Translate from algebra into English:

ⓐ $19 \geq 15$ ⓑ $7 = 12 - 5$ ⓒ $15 \div 3 < 8$ ⓓ $y + 3 > 6$

Determine if each is an expression or an equation:

ⓐ $2 \left(x + 3\right) = 10$ ⓑ $4 \left(y - 1\right) + 1$ ⓒ $x \div 25$ ⓓ $y + 8 = 40$

Determine if each is an expression or an equation: ⓐ $3 \left(x - 7\right) = 27$ ⓑ $5 \left(4 y - 2\right) - 7$.

Determine if each is an expression or an equation: ⓐ $y^{3} \div 14$ ⓑ $4 x - 6 = 22$.

Simplify: $3^{4} .$

Simplify: ⓐ $5^{3}$ ⓑ $1^{7} .$

Simplify: ⓐ $7^{2}$ ⓑ $0^{5} .$

Simplify: ⓐ $12 - 5 \cdot 2$ ⓑ $\left(12 - 5\right) \cdot 2 .$

Simplify: ⓐ $8 + 3 \cdot 9$ ⓑ $\left(8 + 3\right) \cdot 9 .$

Simplify: $30 \div 5 + 10 \left(3 - 2\right) .$

Simplify: $70 \div 10 + 4 \left(6 - 2\right) .$

Simplify: $9 + 5^{3} - \left[4 \left(9 + 3\right)\right] .$

Simplify: $7^{2} - 2 \left[4 \left(5 + 1\right)\right] .$

Evaluate $8 x - 3 ,$ when ⓐ $x = 2$ and ⓑ $x = 1 .$

Evaluate $4 y - 4 ,$ when ⓐ $y = 3$ and ⓑ $y = 5 .$

Evaluate $x = 3 ,$ when ⓐ $x^{2}$ ⓑ $4^{x} .$

Evaluate $x = 6 ,$ when ⓐ $x^{3}$ ⓑ $2^{x} .$

Evaluate $3 x^{2} + 4 x + 1$ when $x = 3 .$

Evaluate $6 x^{2} - 4 x - 7$ when $x = 2 .$

Identify the coefficient of each term: ⓐ 14y ⓑ $15 x^{2}$ ⓒ a.

Identify the coefficient of each term: ⓐ $17 x$ ⓑ $41 b^{2}$ ⓒ z.

Identify the coefficient of each term: ⓐ 9p ⓑ $13 a^{3}$ ⓒ $y^{3} .$

Identify the like terms: $y^{3} ,$ $7 x^{2} ,$ 14, 23, $4 y^{3} ,$ 9x, $5 x^{2} .$

Identify the like terms: $9 ,$ $2 x^{3} ,$ $y^{2} ,$ $8 x^{3} ,$ $15 ,$ $9 y ,$ $11 y^{2} .$

Identify the like terms: $4 x^{3} ,$ $8 x^{2} ,$ 19, $3 x^{2} ,$ 24, $6 x^{3} .$

Identify the terms in each expression.

1. ⓐ $9 x^{2} + 7 x + 12$
2. ⓑ $8 x + 3 y$

Identify the terms in the expression $4 x^{2} + 5 x + 17 .$

Identify the terms in the expression $5 x + 2 y .$

Simplify: $3 x^{2} + 7 x + 9 + 7 x^{2} + 9 x + 8 .$

Simplify: $4 y^{2} + 5 y + 2 + 8 y^{2} + 4 y + 5 .$

Translate the English phrase into an algebraic expression: ⓐ the difference of $14 x^{2}$ and 13 ⓑ the quotient of 12x and 2.

Translate the English phrase into an algebraic expression: ⓐ the sum of $17 y^{2}$ and $19$ ⓑ the product of $7$ and $y .$

Translate the English phrase into an algebraic expression: ⓐ Seventeen more than y ⓑ Nine less than $9 x^{2} .$

Translate the English phrase into an algebraic expression: ⓐ Eleven more than $x$ ⓑ Fourteen less than $11 a .$

Translate the English phrase into an algebraic expression: ⓐ 13 more than z ⓑ 18 less than 8x.

Translate the English phrase into an algebraic expression: ⓐ five times the sum of m and n ⓑ the sum of five times m and n.

Translate the English phrase into an algebraic expression: ⓐ four times the sum of p and q ⓑ the sum of four times p and q.

Translate the English phrase into an algebraic expression: ⓐ the difference of two times x and 8, ⓑ two times the difference of x and 8.

The length of a rectangle is 6 less than the width. Let w represent the width of the rectangle. Write an expression for the length of the rectangle.

The length of a rectangle is 7 less than the width. Let w represent the width of the rectangle. Write an expression for the length of the rectangle.

The width of a rectangle is 6 less than the length. Let l represent the length of the rectangle. Write an expression for the width of the rectangle.

June has dimes and quarters in her purse. The number of dimes is three less than four times the number of quarters. Let q represent the number of quarters. Write an expression for the number of dimes.

Geoffrey has dimes and quarters in his pocket. The number of dimes is eight less than four times the number of quarters. Let q represent the number of quarters. Write an expression for the number of dimes.

Lauren has dimes and nickels in her purse. The number of dimes is three more than seven times the number of nickels. Let n represent the number of nickels. Write an expression for the number of dimes.

Translate from algebra to English.

$16 - 9$

Translate from algebra to English.

$28 \div 4$

Translate from algebra to English.

$\left(2\right) \left(7\right)$

Translate from algebra to English.

$14 < 21$

Translate from algebra to English.

$36 \geq 19$

Translate from algebra to English.

$y - 1 > 6$

Translate from algebra to English.

$2 \leq 18 \div 6$

Determine if each is an expression or an equation.

$9 \cdot 6 = 54$

Determine if each is an expression or an equation.

$5 \cdot 4 + 3$

Determine if each is an expression or an equation.

$x + 9$

Simplify each expression.

$5^{3}$

Simplify each expression.

$2^{8}$

Simplify using the order of operations.

ⓐ $3 + 8 \cdot 5$ ⓑ $\left(3 + 8\right) \cdot 5$

Simplify using the order of operations.

$2^{3} - 12 \div \left(9 - 5\right)$

Simplify using the order of operations.

$3 \cdot 8 + 5 \cdot 2$

Simplify using the order of operations.

$2 + 8 \left(6 + 1\right)$

Simplify using the order of operations.

$4 \cdot 12 / 8$

Simplify using the order of operations.

$\left(6 + 10\right) \div \left(2 + 2\right)$

Simplify using the order of operations.

$20 \div 4 + 6 \cdot 5$

Simplify using the order of operations.

$3^{2} + 7^{2}$

Simplify using the order of operations.

$3 \left(1 + 9 \cdot 6\right) - 4^{2}$

Simplify using the order of operations.

$2 \left[1 + 3 \left(10 - 2\right)\right]$

Evaluate the following expressions.

$7 x + 8$ when $x = 2$

Evaluate the following expressions.

$x^{2}$ when $x = 12$

Evaluate the following expressions.

$x^{5}$ when $x = 2$

Evaluate the following expressions.

$x^{2} + 3 x - 7$ when $x = 4$

Evaluate the following expressions.

$\left(x - y\right)^{2}$ when
$x = 10 , y = 7$

Evaluate the following expressions.

$a^{2} + b^{2}$ when $a = 3 , b = 8$

Evaluate the following expressions.

$2 l + 2 w$ when
$l = 15 , w = 12$

Identify the coefficient of each term.

8a

Identify the coefficient of each term.

$5 r^{2}$

Identify the like terms.

$x^{3} , 8 x , 14 , 8 y , 5 , 8 x^{3}$

Identify the like terms.

$9 a , a^{2} , 16 , 16 b^{2} , 4 , 9 b^{2}$

Identify the terms in each expression.

$15 x^{2} + 6 x + 2$

Identify the terms in each expression.

$10 y^{3} + y + 2$

Simplify the following expressions by combining like terms.

$10 x + 3 x$

Simplify the following expressions by combining like terms.

$4 c + 2 c + c$

Simplify the following expressions by combining like terms.

$7 u + 2 + 3 u + 1$

Simplify the following expressions by combining like terms.

$10 a + 7 + 5 a - 2 + 7 a - 4$

Simplify the following expressions by combining like terms.

$3 x^{2} + 12 x + 11 + 14 x^{2} + 8 x + 5$

Translate the phrases into algebraic expressions.

the difference of 14 and 9

Translate the phrases into algebraic expressions.

the product of 9 and 7

Translate the phrases into algebraic expressions.

the quotient of 36 and 9

Translate the phrases into algebraic expressions.

the sum of 8x and 3x

Translate the phrases into algebraic expressions.

the quotient of y and 3

Translate the phrases into algebraic expressions.

eight times the difference of y and nine

Translate the phrases into algebraic expressions.

Eric has rock and classical CDs in his car. The number of rock CDs is 3 more than the number of classical CDs. Let c represent the number of classical CDs. Write an expression for the number of rock CDs.

Translate the phrases into algebraic expressions.

Greg has nickels and pennies in his pocket. The number of pennies is seven less than twice the number of nickels. Let $n$ represent the number of nickels. Write an expression for the number of pennies.

Car insurance Justin’s car insurance has a $750 deductible per incident. This means that he pays $750 and his insurance company will pay all costs beyond $750. If Justin files a claim for $2,100.

1. ⓐ how much will he pay?
2. ⓑ how much will his insurance company pay?

Explain the difference between an expression and an equation.

Explain how you identify the like terms in the expression $8 a^{2} + 4 a + 9 - a^{2} - 1 .$