How to solve two-step equations - Algebra 1

Card 0 of 20

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

Solve for in terms of .

Answer

First, subtract 7 to both sides.

Factor the y on the left hand side.

Divide both sides by 3 – x.

$y=\frac{-5}{3-x}$

Take an extra step by factoring the minus sign on the denominator.

$y=\frac{-5}{-(x-3)}$

Cancel the minus signs.

$y=\frac{5}{x-3}$

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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 .

$-11 - \frac{6}{x} = 13$

Answer

$-11 - \frac{6}{x} = 13$

Add 11 to each side of the equation.

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

Multiply each side of the equation by .

Divide each side of the equation by 24.

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

Simplify

$-\frac{1}{4}$

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Question

Solve for :

$\small 7x+3=17$

Answer

First, substract 3 from both sides:

$\small 7x+3-3=17-3$

$\small 7x=14$

Next, divide each side by 7:

$\small \frac{7x}{7}= \frac{14}{7}$

$\small x=2$

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Question

A yard stick is cut into two pieces. One piece is 6 inches longer than two times the length of the other piece. Find the length of both pieces, in inches.

Answer

A yard stick has 36 inches. Let length of piece one.

Then, let length of piece two.

The length of both pieces has to be 36 inches.

So,

After combining like terms we get:

Subtracting 6 from both sides gives:

Dividing both sides by 3 gives:, the length of piece one.

The length of piece two is given by

Substituting in gives:

Therefore, the lengths of the two pieces are 10 and 26 inches.

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Question

Solve for .

$\frac{n}{4}-9=9$

Answer

Add 9 to each side of the equation.

$\frac{n}{4}=18$

Multiply each side of the equation by 4.

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Question

Find the value of in the following linear equation and select the correct answer from the choices listed below.

Answer

Solve equation by using inverse order of operations to get by itself.

Order of operations: PEMDAS. Addition and subtraction usually come last, so when using inverse order of operations to "undo an expression," they come first. 8 is being added to , so subtract 8 from both sides in order to get alone.

Next comes multiplication/division. is being multiplied by 2, so divide both sides by 2 to get on its own.

$\frac{2x}{2}=\frac{5}{2}$

$x=\frac{5}{2}$

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Question

Solve for x:

Answer

$x=\frac{49}{5}=9\frac{4}{5}$

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Question

$Solve; for; y ; in ; the; equation,\frac{3y}{2}-\frac{3}{2}=0$

Answer

$Multiply; both; sides ; of; \frac{3y}{2}-\frac{3}{2}=0; by; 2$ $2\times \frac{3y}{2}-2\times \frac{3}{2}=2\times 0$

$3y-3=2\times 0$

$3y\div 3=3\div3$

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Question

Solve for :

$\frac{4}{5}x-12=\frac{4}{3}x+13$

Answer

$\frac{4}{5}x-12=\frac{4}{3}x+13$

$\frac{4}{5}x-\frac{4}{3}x=25$

$\frac{12}{15}x-\frac{20}{15}x=25$

$-\frac{8}{15}x=25$

$x=\frac{-15}{8}\cdot\frac{25}{1}=\frac{-375}{8}=-46\frac{7}{8}$

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Question

Solve this equation:

Answer

Begin by multiplying out all of the terms by the distributive property:

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

Add to both sides of the equation:

, or

Add 3 to both sides:

, or

Finally, divide both sides by 13 to give the final answer:

$a =- \frac{15}{13}$

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Question

Solve for

Answer

First subtract 4 from both sides. This gives . Then divide both sides by 4 to get

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Question

Solve for the value of .

Answer

For the equation , a set of two operations can be used to determine the value of .

First, subtract from both sides of the equation to isolate the variable with its coefficient.

Second, divide both sides of the equation by the coefficient to isolate the variable and its value.

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

The value of is .

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Question

Solve for .

$5x^{2}=80$

Answer

Divide each side of the equation by 5.

$x^{2}=16$

Take the square root of each side of the equation.

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Question

Solve for in the equation below.

Answer

Use the distributive property to eliminate the parantheses.

Combine like terms.

Now we need to isolate . We can add to both sides of the equation, then subtract from both sides.

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Question

Solve for .

$\frac{4p}{5}+8 = 4$

Answer

Subtract 8 from each side of the equation.

$\frac{4p}{5}=-4$

Multiply each side of the equation by $\frac{5}{4}$ (the inverse of $\frac{4}{5}$ ).

$p=\frac{-4}{1}\times\frac{5}{4}=\frac{-20}{4}=-5$

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Question

Solve for :

Answer

To solve for , add to both sides to get . Then, divide both sides by to get $x=\frac{c+b}{a}$ .

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