Linear Equations - Algebra

Card 0 of 11961

Question

Solve

Answer

Solving for a one-step linear equation is simple. All you're being asked is to solve for x. In other words, how do you get x by itself on one side of the equals sign?

In order to solve for these kind of problems, it's important to keep in mind that what you do to one side must be done to the other.

for , we want to get x by itself. The fastest way would be to move the from left of the equals sign to the right with .

This can be accomplished by subtracting from both sides.

$x+21{\color{Blue} -21}=26{\color{Blue} -21}$

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Question

Solve for :

Answer

Subtract 53 from each side of the equation to get by itself:

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Question

Evaluate the expression (3x + 4y)3 when x = 4 and y = 2.

Answer

Plug in 4 for x and 2 for y, giving you (3(4) + 4(2))3, which equals (20)3, equalling 8000.

(3x + 4y)3

(3(4) + 4(2))3

(12 + 8)3

(20)3 = 8000

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Question

Evaluate $(x+3)^2-\frac{18}{2}$ when x = 3.

Answer

First plug 3 in for x, giving you $(6)^2-\frac{18}{2}$ . You square 6, giving you 36, then subtract (18/2), giving you 27.

$(x+3)^2-\frac{18}{2}$

$(3+3)^2-\frac{18}{2}$

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Question

Express the sum of and is forty.

Answer

Take every word and translate into math. Sum is addition. Is means equal sign. So we have .

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Question

Solve for .

Answer

Add 5 to each side of the equation.

Add 3x to each side of the equation.

Divide each side of the equation by 5.

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Question

Solve for .

Answer

Subtract 9 from both sides of the equation.

Divide each side of the equation by 3.

$n=\frac{-9}{3}$

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Question

Solve for .

$\frac{1}{x}=\frac{7}{9}$

Answer

Let's cross multiply.

$\frac{1}{x}=\frac{7}{9}$

We have

$\7\cdot x=1\cdot 9\7x=9$ .

Divide both sides by , we get

$x=\frac{9}{7}$ .

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Question

Solve for .

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

Answer

Let's cross multiply.

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

We have

$\3x\cdot 6=5 \18x=5$ .

Divide both sides by , we get

$x=\frac{5}{18}$ .

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Question

Solve for :

$4=\frac{9}{5x}$

Answer

Let's cross multiply.

$4=\frac{9}{5x}$

We have

$\4\cdot 5x=9\20x=9$ .

Divide both sides by , we have

$x=\frac{9}{20}$ .

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Question

Solve for .

$\frac{1}{x}=3$

Answer

Let's cross multiply.

$\frac{1}{x}=3$

We have

.

Divide both sides by , we have

$x=\frac{1}{3}$ .

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Question

Solve for .

$\frac{1}{1+x}=2$

Answer

Let's cross multiply and distribute the .

$\frac{1}{1+x}=2$

We have .

Subtract both sides by and divide both sides by .

$x=\frac{-1}{2}$

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Question

$\begin{vmatrix} 2x + 4 \end{vmatrix} = 16$

Answer

Absolute value symbols tell you to take whatever number is inside the absolute value and make it positive. This is important to remember for equations with variables like x because if the variable is inside the absolute value symbols, that means two values for the variable will give the right answer. You solve for both the positive and the negative of whatever number is on the other side of the equation, since the absolute value symbols will turn both positive and negative numbers into positive ones. For example, in this problem, the absolute value of 2x+4 is alone on one side of the equation with a variable (x) in it. Set 2x+4 equal to both 16 and -16 in two different equations removing the absolute value sign.

You should have and . Solve to get x alone.

Subtract 4 from both sides of the equation to get

and

Divide by 2 on both sides of the equation to get

and

If you want to check these answers plug them back into the original equation.

$\begin{vmatrix} 26+4 \end{vmatrix}=16$
$\begin{vmatrix} 12+4 \end{vmatrix}=16$
$\begin{vmatrix} 16 \end{vmatrix}=16$

Now try the other solution.

$\begin{vmatrix} 2-10+4 \end{vmatrix}=16$
$\begin{vmatrix} -20+4 \end{vmatrix}=16$
$\begin{vmatrix} -16 \end{vmatrix}=16$

Both solutions for x check out to give the answer 16.

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Question

Solve the equation:

Answer

Isolate the $\textup{x-variable}$ by subtracting on both sides.

Simplify both sides.

The answer is:

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Question

Solve the equation:

Answer

To isolate the x-variable, we will need to add 17 on both sides.

When adding a positive number with a negative number, the final number will be closer to zero.

Simplify both sides.

The answer is:

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Question

Solve the equation:

Answer

In order to isolate the variable, add 55 on both sides.

Simplify both sides of the equation.

The answer is:

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Question

Solve the equation:

Answer

To isolate the x-variable, divide both sides by six.

$\frac{6x}{6}=\frac{63}{6}$

Cancel the sixes on the left and rewrite the right side using common factors.

$x=\frac{3\times 21}{3 \times 2}$

Cancel the threes.

The answer is: $\frac{21}{2}$

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Question

$\begin{vmatrix} -x \end{vmatrix} = 9$

Answer

This problem should be easy if you have a basic understanding of absolute values. Knowing that absolute values make whatever numbers inside them positive, ask yourself, what values for x will equal positive or negative 9? You can again set up two equations.

and

These two equations are already solved for x which means we have our answers.

Double checking by plugging these back into the original equation...

Plugging in 9.

$\begin{vmatrix} -9 \end{vmatrix}=9$

Now to try plugging in -9.

$\begin{vmatrix} -(-9) \end{vmatrix}=9$
$\begin{vmatrix} 9 \end{vmatrix}=9$

Both answers check out

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Question

Convert 16 quarts into gallons.

Answer

To solve this conversion we have to remember that there are 4 quarts per 1 gallon.

In order to have gallons left as our unit, we need to make sure that the other units cancel out by one being in the numerator and one being in the denominator.

Therefore, set up the following conversion and solve:

$\frac{16qts}{1}*\frac{1gal}{4qts}=\frac{16gal}{4}=4gal$

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Question

Harold has a (full) two liter bottle of soda in his refrigerator. He takes it out and pours eight-ounce glasses of soda for himself and each of his three friends that have come over. How many liters of soda are left in the bottle (rounded to two decimal places)?

1 liter = 33.814 fluid ounces

Answer

Convert the two liters of soda into ounces.

Subtract the four eight-ounce glasses of soda that were poured.

Convert the remaining ounces back into liters.

$35.628 * \frac{1}{33.814} = 1.05$

Alternatively, you could set it up as one equation and solve for , as shown below.

$x = 2 - [(8\times 4)\times\tfrac{1}{33.814}]$

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