Solving Equations and Inequalities

Simplify $4\left(14x-10y\right)-6\left(x+4y\right)$

Use the following information.

The product of any two whole numbers is always a whole number. So, the set of whole number is said to be closed under multiplication. This is an example of the Closure Property.

State whether each statement is true or false. If false, given a counterexample.

The set of integers is closed under multiplication. 

Use the following information.

The product of any two whole numbers is always a whole number. So, the set of whole number is said to be closed under multiplication. This is an example of the Closure Property.

State whether each statement is true or false. If false, given a counterexample.

75. The set of whole numbers is closed under subtraction.

Use the following information.

The product of any two whole numbers is always a whole number. So, the set of whole number is said to be closed under multiplication. This is an example of the Closure Property.

State whether each statement is true or false. If false, given a counterexample.

The set of rational numbers is closed under addition. 

Use the following information.

The product of any two whole numbers is always a whole number. So, the set of whole number is said to be closed under multiplication. This is an example of the Closure Property.

State whether each statement is true or false. If false, given a counterexample.

77. The set of whole numbers is closed under division. 

Find the value of each expression

$9{\left(4-3\right)}^5$

Find the value of each expression

79. $5+9÷3\left(3\right)-8$

Evaluate each expression if $a=-5,b=0.25,c=\frac{1}{2},$ and  $d=4$.

80. $a+2b-c$

Evaluate each expression if $a=-5,b=0.25,c=\frac{1}{2},$ and  $d=4$.

81. $b+3{\left(a+d\right)}^3$

GEOMETRY

82. 82. The formula for the surface area SA of a rectangular prism is $SA=2lw+2lh+2wh$, where l represents length, w represents width, and h represents height. Find the surface area of the rectangular prism.

Evaluate each expression if $a=2, b=-\frac{3}{4},$ and $c=1.8$.

$8b-5$

PREREQUISITE SKILL 

Evaluate each expression if $a=2,b=-\frac{3}{4},$ and  $c=1.8$.

84. $\frac{2}{5}b+1$

Evaluate each expression if $a=2, b=-\frac{3}{4},$ and $c=1.8$.

 $1.5c-7$

PREREQUISITE SKILL 

Evaluate each expression if $a=2,b=-\frac{3}{4},$ and c=1.8.

86. $-9\left(a-6\right)$

Write an algebraic expression to represent each verbal expression.

Four less than square of a number

Write an equation whose solution is $-7$.

Write an equation whose solution is $-7$.

Determine whether the following statement is sometimes, always, or never true. Explain.

Dividing each side of an equation by the same expression produces an equivalent equation.

FIND THE ERROR 

 Crystal and Jamal are solving $C=\frac{5}{9}\left(F-32\right)$ for F.

Crystal

$$\begin{gathered} C=\frac{5}{9}(F-32) \\ C+32=\frac{5}{9}F \\ \frac{9}{5}(C+32)=F \end{gathered}$$

Jamal

$$\begin{gathered} C=\frac{5}{9}(F-32) \\ \frac{9}{5}C=F-32 \\ \frac{9}{5}C+32=F \end{gathered}$$

Write an algebraic expression to represent each verbal expression.

Five increased by four times a number

Write an algebraic expression to represent each verbal expression.

Twice a number decreased by the cube of the same number

Write a verbal expression to represent each equation.

$9n-3=6$

Write a verbal expression to represent each equation.

$5+3x^2=2x$

Name the property illustrate by each statement.

$\left(3x+2\right)-5=\left(3x+2\right)-5$

Name the property illustrate by each statement.

If $4c=15$, then $4c+2=15+2$.

Solve each equation. Check your solution.

$y+14=-7$

Solve each equation. Check your solution.

$7+3x=49$

Solve each equation. Check your solution.

$-4\left(b+7\right)=-12$

Solve each equation. Check your solution.

$7q+q-3q=-24$

Solve each equation. Check your solution.

$1.8a-5=-2.3$

Solve each equation. Check your solution.

$-\frac{3}{4}n+1=-11$

Solve each equation or formula for the specified variable.

$4y-2n=9$, for y.

Solve each equation or formula for the specified variable.

$I=prt$, for p.

If $4x+7=18$, what is the value of $12x+21$?

A. $2.75$

B. 32

C. 33

D. 54

Write an algebraic expression to represent each verbal expression.

The sum of 5 and three times a number

Write an algebraic expression to represent each verbal expression.

Seven more than the product of a number and 10

Write an algebraic expression to represent each verbal expression.

The product of the cube of a number and$-6$

Write an algebraic expression to represent each verbal expression.

Five times the sum of 9 and a number

Write an algebraic expression to represent each verbal expression.

Seven more than the product of a number and 10

Write an algebraic expression to represent each verbal expression.

Twice the sum of a number and 8

Write an algebraic expression to represent each verbal expression.

The square of the quotient of a number and 4

Write an algebraic expression to represent each verbal expression.

The cube of the difference of a number and 7

The formula for the surface area of a cylinder with radius r and height h is $\pi$ times twice the product of the radius and height plus twice the product of $\pi$and the square of the radius

Translate this verbal expression of the formula into an algebraic expression.

The formula for the surface area of a cylinder with radius r and height h is $\pi$ times twice the product of the radius and height plus twice the product of $\pi$.and the square of the radius.

Write an equivalent expression using the Distributive Property.

Write a verbal expression to represent each equation.

$2n+3=-1$

Write a verbal expression to represent each equation.

$y^2=4y$

Write a verbal expression to represent each equation.

$3a^3=a+4$

Write a verbal expression to represent each equation.

$\frac{b}{4}=2\left(b+1\right)$

Write a verbal expression to represent each equation.

$7-\frac{1}{2}x=\frac{3}{x^2}$

Write a verbal expression to represent each equation.