Linear Equations - College Algebra

Card 0 of 16

Question

Solve for :

Answer

can be simplified to become

Then, you can further simplify by adding 5 and to both sides to get .

Then, you can divide both sides by 5 to get .

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Question

Solve the following equation for :

Answer

The first step is to distribute (multiply) the 2 through the parentheses:

Then isolate on the left side of the equation. Subtract the 10 from the left and right side.

Finally, to isolate , divide the left side by 2 so that the 2 cancels out. Then divide by 2 on the right side as well.

You can verify this answer by plugging the into the original equation.

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Question

Solve for :

Answer

Combine like terms on the left side of the equation:

Use the distributive property to simplify the right side of the equation:

Next, move the 's to one side and the integers to the other side:

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Question

Solve for :

Answer

To solve for , you must first combine the 's on the right side of the equation. This will give you $\ 6x-1=9x+8$ .

Then, subtract and from both sides of the equation to get .

Finally, divide both sides by to get the solution .

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Question

Solve for x:

Answer

Simplify the parenthesis:

Combine the terms with x's:

Combine constants:

$7x=35\rightarrow \mathbf{x=5}$

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Question

Solve the following equation when y is equal to four.

Answer

Solve the following equation when y is equal to four.

To solve this equation, we need to plug in 4 for y and solve.

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Question

Solve the following:

Answer

To solve, we must isolate x. In order to do that, we must first add 7 to both sides.

Next, we must divide both sides by 3.

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

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Question

Write an equation of the line passing through (5,10) and (10,2).

Answer

To find this line, first find the slope (m) between the two coordinate points. Then use the point-slope formula to find a line with that same slope passing through a particular point.

$m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}= \frac{2-10}{10-5}=-\frac{8}{5}$

$y-y_{1}=m(x-x_{1})$

$y-10=-\frac{8}{5}(x-5) \rightarrow y-10=-\frac{8}{5}x+8 \rightarrow \boldsymbol{y=-\frac{8}{5}x+18}$

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Question

Solve for .

Answer

First distribute out each side of the equation.

simplifies to .

Now for the right hand side,

becomes .

Now we equate both sides.

,

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Question

Solve for .

Answer

First, we need to simplify what's inside the parentheses.

Now we continue to evaluate the left hand side.

The right hand side does not need any reduction.

We set the two sides equal to each other.

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Question

Solve the equation: $3x = -\frac{1}{18}$

Answer

In order to isolate the x-variable, we will need to multiply both sides by one third.

$3x \cdot \frac{1}{3}= -\frac{1}{18} \cdot \frac{1}{3}$

Simplify both sides.

$x= -\frac{1}{54}$

The answer is: $-\frac{1}{54}$

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Question

Evaluate:

Answer

Add on both sides.

Add one on both sides.

Divide by 16 on both sides.

$\frac{7}{16}=\frac{16x}{16}$

The answer is: $\frac{7}{16}$

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Question

Express the following linear inequality in interval notation.

$7-2x\geq1$

Answer

Upon solving for x, we find that x is less than or equal to 3. The left-hand term of the interval is negative infinity since any number less than 3 is in our set, and infinity always has a parenthesis around it. The right-hand term of the interval is 3 since it is the upper bound of our set. There is a bracket around it because 3 is included in our set (3 is less than or equal to 3). Remember when dividing or multiplying by a negative number in an inequality to reverse the direction of the inequality.

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Question

Solve:

Answer

Step 1: Subtract 6 from both sides...

Step 2: Divide by 2.

$\frac {2x}{2}=\frac {6}{2}$

Simplify:

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Question

Solve: (positive roots only)

Answer

Step 1: Subtract from both sides

Step 2: Simplify:

Step 3: Divide..

$\frac {2x^2}{2}=\frac {8}{2}$

Step 4: Take the square root of both sides...

$\sqrt{x^2}=\sqrt{4}$

Step 5: Simplify and get the answer...

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Question

Solve:

Answer

Move to the other side by subtracting it from both sides.

Simplify:

Divide by the coefficient, the number in front of x.

$\frac {4x}{4}=\frac {8}{4}$

Reduce:

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