Open Sentences and Identities

Some examples of open sentences include;

$5+n=12$

Find the solution for the equation, $3x+6=18$ if the replacement set is {2, 4, 6, 8}

Solution:

To solve this you can start by substituting each option from the replacement set into the equation to find out if any of them create a true sentence;

$3\left(2\right)+6=12$

$\mathbf{3}\mathbf{\left(}\mathbf{4}\mathbf{\right)}\mathbf{+}\mathbf{6}\mathbf{=}\mathbf{18}$

$3\left(6\right)+6=24$

$3\left(8\right)+6=30$

Here you can see that the sentence is true when$x=4$ therefore the solution set is {4}.

Find the solution for the equation, $6(x+4)=60$ if the replacement set is {2, 4, 6, 8}

Solution:

Once again simply substitute each variable from the replacement set to find your solution;

$6\left(\right(2)+4)=36$

$6\left(\right(4)+4)=48$

$\mathbf{6}\mathbf{\left(}\mathbf{\right(}\mathbf{6}\mathbf{)}\mathbf{+}\mathbf{4}\mathbf{)}\mathbf{=}\mathbf{60}$

$6\left(\right(8+4)=72$

Here you can see that the sentence is true when$x=6$, therefore your solution set is {6}.

Find the solution for the equation, $12-2x=-4$ if the replacement set is {2, 4, 6, 8}

Solution:

Start by substituting each of the variables into the equation;

$12-2\left(2\right)=8$

$12-2\left(4\right)=4$

$12-2\left(6\right)=0$

$\mathbf{12}\mathbf{-}\mathbf{2}\mathbf{\left(}\mathbf{8}\mathbf{\right)}\mathbf{=}\mathbf{-}\mathbf{4}$

Here you can see that the sentence is true when$x=8$, therefore the solution set is {8).

$10+0=10$

$5\times 1=5$

$12\times 0=0$

$\frac{1}{5}\times 5=1$

Find the value of x and identify what property is being used, $25\times x=25$

Solution:

You know that the multiplicative identity says that a number is multiplied by 1 the product is the number, therefore $x=1$.

Find the value of x and identify what property is being used, $32+x=32$

Solution:

You know that the additive identity says that when you add 0 to a number, the sum is the number, therefore$x=0$.

Find the value of x and identify what property is being used, $2\times x=1$

Solution:

The multiplicative inverse property is applied when the product of two numbers equals 1. This means that$x=\frac{1}{2}$.