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Algebra 1 : Linear Equations

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Example Questions

Example Question #1 : How To Solve One Step Equations

What is the solution of 3x = 9?

Possible Answers:

–6

1/3

–3

Correct answer:

Explanation:

When solving a one step equation like this, we do the inverse operation to isolate the variable. In this case, we have 3x = 9, so we divide both sides by 3 to get x = 3.

3x = 9

(3x)/3 = (9)/3

x = 3

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Example Question #1 : Linear Equations

Identify the imaginary part of the following complex number:

1-3i $\displaystyle 1-3i$

Possible Answers:

$\displaystyle -3$

1-3i $\displaystyle 1-3i$

$\displaystyle -2$

$\displaystyle i$

$\displaystyle 1$

Correct answer:

$\displaystyle -3$

Explanation:

A complex number in its standard form is of the form: a+bi $\displaystyle a+bi$ , where $\displaystyle a$ stands for the real part and $\displaystyle b$ stands for the imaginary part. The symbol $\displaystyle i$ stands for $\sqrt{-1}$ $\displaystyle \sqrt{-1}$ .

The imaginary part is $\displaystyle -3$ .

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Example Question #2 : How To Solve One Step Equations

Find the conjugate of 1-3i $\displaystyle 1-3i$ .

Possible Answers:

3i-1 $\displaystyle 3i-1$

$\displaystyle 1$

1+3i $\displaystyle 1+3i$

1-3i $\displaystyle 1-3i$

$\displaystyle 3i$

Correct answer:

1+3i $\displaystyle 1+3i$

Explanation:

The conjugate is 1+3i $\displaystyle 1+3i$ so that when 1-3i $\displaystyle 1-3i$ is multiplied by its conjugate we get

$1^{2}-\left (3i^{} \right )^{2} = 1 - 9\left ( i^{2} \right )$ $\displaystyle 1^{2}-\left (3i^{} \right )^{2} = 1 - 9\left ( i^{2} \right )$

Since $i^{2}= -1$ $\displaystyle i^{2}= -1$

we get

$\displaystyle 1-9(-1)=10$ .

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Example Question #3 : How To Solve One Step Equations

Identify the real part of -3i $\displaystyle -3i$ .

Possible Answers:

$\displaystyle 0$

$\displaystyle -3$

$\displaystyle i$

$\displaystyle -i$

$\displaystyle 3$

Correct answer:

$\displaystyle 0$

Explanation:

The real part is 0.

In this problem there is no real part. Hence the real part equals 0.

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Example Question #1 : Algebra 1

Identify the imaginary part of -3i $\displaystyle -3i$ .

Possible Answers:

$\displaystyle i$

$\displaystyle -3$

$\displaystyle -i$

$\displaystyle 3$

$\displaystyle 0$

Correct answer:

$\displaystyle -3$

Explanation:

The imaginary part equals $\displaystyle -3$ based on the definition of a complex number in standard form which is a+bi $\displaystyle a+bi$ .

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Example Question #4 : How To Solve One Step Equations

Identify the conjugate of -3i $\displaystyle -3i$ .

Possible Answers:

$\displaystyle -3$

$\displaystyle 3i$

-3i $\displaystyle -3i$

$\displaystyle -i$

$\displaystyle i$

Correct answer:

$\displaystyle 3i$

Explanation:

The conjugate of an imaginary number is the opposite of the given imaginary part. For example the conjugate of $\displaystyle 3i$ is -3i $\displaystyle -3i$ and conjugate of -3i $\displaystyle -3i$ equals $\displaystyle 3i$

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Example Question #1 : Algebra 1

Find the conjugate of $\displaystyle -4$ .

Possible Answers:

$\displaystyle -i$

-4i $\displaystyle -4i$

$\displaystyle -4$

$\displaystyle i$

$\displaystyle 4i$

Correct answer:

$\displaystyle -4$

Explanation:

Since $\displaystyle -4$ is a real number its conjugate is also $\displaystyle -4$ .

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Example Question #5 : How To Solve One Step Equations

Solve for $\displaystyle x$ :

$\frac{4}{3}x-\frac{5}{6}=4$ $\displaystyle \frac{4}{3}x-\frac{5}{6}=4$

Possible Answers:

$4\frac{2}{3}$ $\displaystyle 4\frac{2}{3}$

$5\frac{1}{8}$ $\displaystyle 5\frac{1}{8}$

None of the available answers

$3\frac{5}{6}$ $\displaystyle 3\frac{5}{6}$

$3\frac{5}{8}$ $\displaystyle 3\frac{5}{8}$

Correct answer:

$3\frac{5}{8}$ $\displaystyle 3\frac{5}{8}$

Explanation:

$\frac{4}{3}x-\frac{5}{6}=4$ $\displaystyle \frac{4}{3}x-\frac{5}{6}=4$

First we will add $\frac{5}{6}$ $\displaystyle \frac{5}{6}$ to both sides.

$\frac{4}{3}x=4+\frac{5}{6}$ $\displaystyle \frac{4}{3}x=4+\frac{5}{6}$

$\frac{4}{3}x=4\frac{5}{6}$ $\displaystyle \frac{4}{3}x=4\frac{5}{6}$

Then we will multiple both sides by $\frac{3}{4}$ $\displaystyle \frac{3}{4}$ to isolate $\displaystyle x$ .

$x=4\frac{5}{6}\cdot\frac{3}{4}=(4+\frac{5}{6})\cdot\frac{3}{4}=\frac{12}{4}+\frac{15}{24}=3\frac{15}{24}=3\frac{5}{8}$ $\displaystyle x=4\frac{5}{6}\cdot\frac{3}{4}=(4+\frac{5}{6})\cdot\frac{3}{4}=\frac{12}{4}+\frac{15}{24}=3\frac{15}{24}=3\frac{5}{8}$

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Example Question #2 : How To Solve One Step Equations

Solve for $\displaystyle x$ :

x+17=12 $\displaystyle x+17=12$

Possible Answers:

$\displaystyle -29$

$\displaystyle 29$

$\displaystyle -5$

$\displaystyle 5$

$\displaystyle 15$

Correct answer:

$\displaystyle -5$

Explanation:

$\displaystyle x+17-17=12-17$

x=-5 $\displaystyle x=-5$

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Example Question #6 : How To Solve One Step Equations

What is the value of $\displaystyle x$ ?

$\displaystyle x+5=3x-1$

Possible Answers:

$\displaystyle 3$

$\displaystyle 5$

$\displaystyle 2$

$\displaystyle 1$

$\displaystyle 4$

Correct answer:

$\displaystyle 3$

Explanation:

Simplifying for $\displaystyle x+5=3x-1$ gives you 2x=6 $\displaystyle 2x=6$ . Thus, the value of $\displaystyle x$ is 3.

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Algebra 1 : Linear Equations

Study concepts, example questions & explanations for Algebra 1

All Algebra 1 Resources

Example Questions

Example Question #1 : How To Solve One Step Equations

Example Question #1 : Linear Equations

Example Question #2 : How To Solve One Step Equations

Example Question #3 : How To Solve One Step Equations

Example Question #1 : Algebra 1

Example Question #4 : How To Solve One Step Equations

Example Question #1 : Algebra 1

Example Question #5 : How To Solve One Step Equations

Example Question #2 : How To Solve One Step Equations

Example Question #6 : How To Solve One Step Equations

All Algebra 1 Resources

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