How to solve one-step equations - Algebra

Card 0 of 4788

Question

Solve for :

Answer

Add to both sides.

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Question

Solve for :

Answer

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Question

Solve for :

$\frac{3}{4}x=12$

Answer

$\frac{3}{4}x=12$

Multiply both sides by $\frac{4}{3}$ .

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Question

Solve for :

$\frac{x}{6}=24$

Answer

$\frac{x}{6}=24$

Multiply both sides by .

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Question

What is the solution of 3x = 9?

Answer

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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Question

Solve for .

Answer

Add 15 to each side of the equation.

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Question

Identify the imaginary part of the following complex number:

Answer

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

The imaginary part is .

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Question

Find the conjugate of .

Answer

The conjugate is so that when is multiplied by its conjugate we get

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

Since $i^{2}= -1$

we get

.

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Question

Identify the real part of .

Answer

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

The real part is 0.

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

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Question

Identify the imaginary part of .

Answer

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

The imaginary part equals based on the definition of a complex number in standard form which is .

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Question

Identify the conjugate of .

Answer

The conjugate of an imaginary number is the opposite of the given imaginary part. For example the conjugate of is and conjugate of equals

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Question

Find the conjugate of .

Answer

Since is a real number its conjugate is also .

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Question

Solve for :

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

Answer

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

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

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

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

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

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

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Question

Answer

$\fn_cm Divide ; both;sides;of;-4 w = 12;by;-4$ $w = 12\div (-4)$
$=\frac{4\times 3}{-4}=\frac{3}{-1}=-3$

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Question

$Solve; for; p; in; -\frac{p}{7} = \frac{7}{2}$

Answer

$Multiply; both; sides; of; -\frac{p}{7} = \frac{7}{2}; by ; -7$ $\fn_cm \fn_cm \frac{-7p}{-7} = \frac{-7\times7 }{2}$
$\fn_cm p=\frac{-49}{2}$

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Question

What is the value of ?

Answer

Simplifying for gives you . Thus, the value of is 3.

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Question

What is the smaller root of ?

Answer

To determine the roots of the equation, you must set each expression equal to 0. In this case, there are two expressions being multiplied. Thus, you must set and , which would give you and as roots, with being the smaller root.

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Question

Solve for :

Answer

Simplify the equation to get . Simplify further to get , which then gives you .

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Question

Solve for .

Answer

Multiply the terms in parentheses using the distributive property.

Then, combine like terms on both sides of the equation.

Then, put the terms on the left and the integers on the right:

Divide both sides by two to isolate .

$x = \frac{13}{2}$

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Question

Solve for $\small x$ .

Answer

Add 8 to both sides.

Simplify.

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