Chapter 2, Problem 1RE

Label the following as either an expression or an equation:

a. $3x+y=10$ b. $9z+10x-2xy$

c. $4(x+3)=12$ d. $-5x=7$

To determine

Whether the mathematical statement $3x+y=10$ is an expression or an equation.

Answer to Problem 1RE

Solution:

The provided mathematical statement $3x+y=10$ is an equation.

Explanation of Solution

Given Information:

The mathematical statement, $3x+y=10$.

An expression is a mathematical statement which can contain variables, number and operations.

And, an equation is an algebraic statement which indicates that the two expressions are equal.

Now, consider the mathematical statement $3x+y=10$.

The above mathematical statement indicates that two expressions $3x+y$ is equal to 10. Hence, the mathematical statement $3x+y=10$ is an equation.

To determine

Whether the mathematical statement $9x+10x-2xy$ is an expression or an equation.

Answer to Problem 1RE

Solution:

The provided mathematical statement $9x+10x-2xy$ is an expression.

Explanation of Solution

Given Information:

The mathematical statement, $9x+10x-2xy$.

An expression is a mathematical statement which can contain variables, number and operations.

And, an equation is an algebraic statement which indicates that the two expressions are equal.

Now, consider the mathematical statement $9x+10x-2xy$.

The above mathematical statement does not have any equal sign. It is just a mathematical symbol with variable x and y, numbers 9,10 and 2 and operation addition and subtraction. Hence, the mathematical statement $9x+10x-2xy$ is an expression.

To determine

Whether the mathematical statement $4\left(x+3\right)=12$ is an expression or an equation.

Answer to Problem 1RE

Solution:

The provided mathematical statement $4\left(x+3\right)=12$ is an equation.

Explanation of Solution

Given Information:

The mathematical statement, $4\left(x+3\right)=12$.

An expression is a mathematical statement which can contain variables, number and operations.

And, an equation is an algebraic statement which indicates that the two expressions are equal.

Now, consider the mathematical statement $4\left(x+3\right)=12$.

The above mathematical statement indicates that two expressions $4\left(x+3\right)$ is equal to 12. Hence, the mathematical statement $4\left(x+3\right)=12$ is an equation.

To determine

Whether the mathematical statement $-5x=7$ is an expression or an equation.

Answer to Problem 1RE

Solution:

The provided mathematical statement $-5x=7$ is an equation.

Explanation of Solution

Given Information:

The mathematical statement, $-5x=7$.

An expression is a mathematical statement which can contain variables, number and operations.

And, an equation is an algebraic statement which indicates that the two expressions are equal.

Now, consider the mathematical statement $-5x=7$.

The above mathematical statement indicates that two expressions $-5x$ is equal to 7. Hence, the mathematical statement $-5x=7$ is an equation.