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Algebra 1 : Linear Equations

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Example Questions

Example Question #251 : How To Solve One Step Equations

Solve for : 4x=11 .

Possible Answers:

$\frac{11}{4}$

$-\frac{4}{11}$

$\frac{4}{11}$

None of the above

$-\frac{11}{4}$

Correct answer:

$\frac{11}{4}$

Explanation:

In order to solve for in the above equation, we must isolate it on one side of the equation. We can do this by applying an operation to that is the inverse (opposite) of what's currently being applied to .

Given 4x=11 , we see that is being multiplied by , so we need to divide both sides of the equation by to isolate :

4x=11

$\frac{4x}{4}=\frac{11}4{}$

$x=\frac{11}{4}$

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Example Question #251 : Linear Equations

Solve for :

23 + x = 40

Possible Answers:

Correct answer:

Explanation:

In order to solve 23 + x = 40 , we need to get all by itself on one side of the equal sign. To do this, we need to subtract from both sides of the equation:

(23+ x) - 23 = (40)-23

23 - 23 = 0 , so is left by itself on the left side of the equal sign, and 40 - 23 = 17 , leaving us with on the right side of the equal sign:

x=17

So, our solution to this problem is .

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Example Question #252 : Linear Equations

6x=-72

Possible Answers:

x=-12

x=-78

x=78

x=-66

x=12

Correct answer:

x=-12

Explanation:

To solve a one-step equation, we first determine what is being done to the variable in the equation and then do the inverse of that. Here is being multiplied by , so we must do the inverse: divide by .

6x=-72 .

After dividing both sides by , we get:

x=-12 .

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Example Question #252 : How To Solve One Step Equations

Solve for : 3x=9 .

Possible Answers:

$\frac{1}{3}$

Correct answer:

Explanation:

Given 3x=9 , we see that is being multiplied by , so we need to divide both sides of the equation by to isolate :

3x=9

$\frac{3x}{3}=\frac{9}{3}$

x=3

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Example Question #251 : Linear Equations

Solve for : $\frac{1}{4}x=25$ .

Possible Answers:

$\frac{4}{25}$

$\frac{25}{4}$

100

Correct answer:

100

Explanation:

Given $\frac{1}{4}x=25$ , we see that is being multiplied by $\frac{1}{4}$ , so we need to divide both sides of the equation by $\frac{1}{4}$ (or multiply by , equivalently) to isolate :

$\frac{1}{4}x=25$

$(4)\frac{1}{4}x=25(4)$

x=100

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Example Question #253 : Linear Equations

Solve for : $\frac{x}{3} = 2$

Possible Answers:

x = 5

x = 6

$x = \frac{3}{2}$

$x = \frac{2}{3}$

x = 4

Correct answer:

x = 6

Explanation:

Because $\frac{x}{3}$ is a fraction with the variable in the numerator, we want to isolate it by multiplying both sides of our equation by the denominator.

$\frac{x}{3} \cdot 3 = 2 \cdot 3$

Now we can cancel the s on the left half, and solve for the right half.

x = 6

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Example Question #254 : Linear Equations

Solve for : 18 = s+7

Possible Answers:

s=11

s=25

$s = \frac{18}{7}$

s = 126

Correct answer:

s=11

Explanation:

To solve this equation by isolating the variable, subtract the term that is not the variable from both sides.

18 -7 = s+7 - 7 Subtract from both sides.

Now, simplify the equation.

11 = s

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Example Question #255 : Linear Equations

Solve for : 3z = 33

Possible Answers:

z = 11

z = 99

z = 36

z = 30

Correct answer:

z = 11

Explanation:

is the same as $3 \cdot z$ , so to isolate our variable we should divide both sides of the equation by :

$\frac{3z}{3} = \frac{33}{3}$ Divide both sides by .

Now, simplify the equations. Remember that $\frac{3z}{3} \neq \frac{3+z}{3}$ .

z = 11

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Example Question #256 : Linear Equations

What property of equality allows us to solve the one-step equation J + 7 = 10 ?

Possible Answers:

Multiplication Property of Equality

Addition Property of Equality

Subtraction Property of Equality

Reflexive Property of Equality

Substitution Property of Equality

Correct answer:

Subtraction Property of Equality

Explanation:

To isolate our variable, we must subtract from each side. We may do so without altering the value of the equation since the Subtraction Property of Equality says that if , then .

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Example Question #257 : Linear Equations

What property of equality allows us to solve the equation 7g = 49 for ?

Possible Answers:

Substitution Property of Equality

Subtraction Property of Equality

Addition Property of Equality

Division Property of Equality

Multiplication Property of Equality

Correct answer:

Division Property of Equality

Explanation:

To solve the equation 7g = 49 , we must isolate by dividing both sides by . This is permissible because of the Division Property of Equality, which states that if , then $\frac{a}{x} = \frac{b}{x}$ , where $x \neq 0$ . (That last bit is just part of a general prohibition on dividing by zero).

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Algebra 1 : Linear Equations

Study concepts, example questions & explanations for Algebra 1

All Algebra 1 Resources

Example Questions

Example Question #251 : How To Solve One Step Equations

Example Question #251 : Linear Equations

Example Question #252 : Linear Equations

Example Question #252 : How To Solve One Step Equations

Example Question #251 : Linear Equations

Example Question #253 : Linear Equations

Example Question #254 : Linear Equations

Example Question #255 : Linear Equations

Example Question #256 : Linear Equations

Example Question #257 : Linear Equations

All Algebra 1 Resources

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