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Basic Arithmetic : Solving Equations with Whole Numbers

Study concepts, example questions & explanations for Basic Arithmetic

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Example Questions

Example Question #1 : Solving Equations With Whole Numbers

Solve for .

2x-6=14

Possible Answers:

x=8

x=4

x=10

x=20

Correct answer:

x=10

Explanation:

First, add 6 to both sides so that the term with "x" is on its own.

2x=20

Now, divide both sides by 2.

x=10

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Example Question #2 : Linear Equations With Whole Numbers

Solve for .

7b-10=4

Possible Answers:

$b=\frac{7}{6}$

b=14

b=2

$b=\frac{6}{7}$

Correct answer:

b=2

Explanation:

Start by isolating the term with to one side. Add 10 on both sides.

7b=14

Divide both sides by 7.

b=2

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Example Question #1 : Solving Equations With Whole Numbers

Solve for t.

7(t-2)=21

Possible Answers:

t=7

t=3

t=35

t=5

Correct answer:

t=5

Explanation:

First start by distributing the 7.

7(t-2)=7t-14

7t-14=21

Now, add both sides by 14.

7t=35

Finally, divide both sides by 7.

t=5

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Example Question #1 : Solving Equations With Whole Numbers

Solve for .

9g-10=71

Possible Answers:

Correct answer:

Explanation:

Start by adding 10 to both sides of the equation.

9g=81

Then, divide both sides by .

g=9

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Example Question #1 : Solving Equations With Whole Numbers

Solve for :

3x-7=14

Possible Answers:

Correct answer:

Explanation:

First, add to both sides of the equation:

3x=21

Then, divide both sides by :

x=7

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Example Question #1 : Solving Equations With Whole Numbers

If $\small \small 6x+9=45$ , what is $\small x$ equal to?

Possible Answers:

$\small x=9$

$\small x=5$

$\small x=1$

$\small x=6$

$\small x=45$

Correct answer:

$\small x=6$

Explanation:

When solving an equation, we need to find a value of x which makes each side equal each other. We need to remember that $\small 6x+9$ is equal to and the same as $\small 45$ . When we solve an equation, if we make a change on one side, we therefore need to make the exact same change on the other side, so that the equation stays equal and true. To illustrate, let's take a numerical equation:

$\small \small 2\times3+4=10$

If we subtract $\small 4$ from each side, the equation still remains equal:

$\small 2\times3+4-4=10-4$

$\small 2\times3=6$

If we now divide each side by $\small 3$ , the equation still remains equal:

$\small \frac{2\times3}{3}=\frac{6}{3}$

$\small 2=2$

This still holds true even if we have variables in our equation. We can perform the inverse operations to isolate the variable on one side and find out what number it's equal to. To solve our problem then, we need to isolate our $\small x$ term. We can do that by subtracting $\small \small 9$ from each side, the inverse operation of adding $\small \small 9$ :

$\small 6x+9-9=45-9$

$\small 6x=36$

We now want there to be one $\small x$ on the left side. $\small 6x$ is the same thing as $\small 6\times x$ , so we can get rid of the 6 by performing the inverse operation on both sides, i.e. dividing each side by $\small 6$ :

$\small \frac{6x}{6}=\frac{36}{6}$

$\small x=6$ is therefore our final answer.

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Example Question #1 : Solving Equations With Whole Numbers

Solve:

-418 + 20x= 42

Possible Answers:

x= 440

x= -18.8

x=23

x=-23

x= 20

Correct answer:

x=23

Explanation:

The answer is x=23 . The goal is to isolate the variable, , on one side of the equation sign and have all numerical values on the other side of the equation.

Since is a negative number, you must add 418 to both sides.

20x = 460

Then, divide both sides of the equation by :

$x=\frac{460}{20} = 23$

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Basic Arithmetic : Solving Equations with Whole Numbers

Study concepts, example questions & explanations for Basic Arithmetic

All Basic Arithmetic Resources

Example Questions

Example Question #1 : Solving Equations With Whole Numbers

Example Question #2 : Linear Equations With Whole Numbers

Example Question #1 : Solving Equations With Whole Numbers

Example Question #1 : Solving Equations With Whole Numbers

Example Question #1 : Solving Equations With Whole Numbers

Example Question #1 : Solving Equations With Whole Numbers

Example Question #1 : Solving Equations With Whole Numbers

All Basic Arithmetic Resources

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