Two-Step Equations with Decimals - Pre-Algebra

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Question

Solve for p:

Answer

$\frac{1.5p}{1.5}=\frac{3.0}{1.5}$

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Question

Solve for :

Answer

Step 1: Subtract from both sides:

Step 2: Divide both sides by :

$\frac{.5x}{.5}= \frac{1.6}{.5}$

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Question

Solve for :

Answer

The goal is to isolate the variable to one side.

Subtract from both sides:

Divide each side by :

$\frac{0.33x}{0.33}=\frac{8.33}{0.33}$

$x=25.\overline{24}$

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Question

Solve for .

Answer

To solve this problem, move all terms with x on one side and all other terms on the other side. We now get

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Question

Solve for :

Answer

Explanation:

Step 1: Subtract from both sides:

Step 2: Divide both sides by :

$\frac{0.75x}{0.75}=\frac{4.5}{0.75}$

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Question

Solve the equation for .

Answer

The correct answer to this question is .

To start, you need to move 's one one side of the equation and numbers to the other side of the equation:

First, you subtract from both sides of the equation. Then, you will have put all of the 's on the same side of the equation:

Next, you add to the left side of the equation to put all of the numbers on the same side of the equation:

Once you do this, you can add the numbers on the left side of the equation together and find that .

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Question

$\frac{x }{3.2}- 1.6 = 5.4$

Answer

$\frac{x }{3.2}- 1.6 = 5.4$

$\frac{x }{3.2}- 1.6 + 1.6= 5.4 + 1.6$

$\frac{x }{3.2} = 7$

$\frac{x }{3.2} \cdot 3.2 = 7\cdot 3.2$

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Question

Solve for :

$\frac{x - 1.6}{3.2} = 10$

Answer

$\frac{x - 1.6}{3.2} = 10$

$\frac{x - 1.6}{3.2} \cdot 3.2 = 10 \cdot 3.2$

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Question

Solve for :

Answer

$2.4x \div 2.4= 9.3 \div 2.4$

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Question

Solve for :

$1.2\left ( 6.4\ y\right ) = 69.12$

Answer

$1.2\left ( 6.4 y\right ) = 69.12$

Use distributive property, multiply and

Divide both sides by

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Question

Solve for x:

Answer

To solve, use inverse opperations: do the opposite steps in the opposite order. Order of opperations is usually PEMDAS, with addition and subtraction last, so we'll do addition/subtraction first:

right now it says to add , so we'll subtract it from both sides.

next we will do multiplication/dividion. Right now it is multiplying by , so we will divide both sides by .

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Question

Solve for :

Answer

The goal is to solve for x. To do this we need to get x by itself. There are two terms on the same side of the equation with the variable we want isolate. We must cancel them out.

Add the term not attached to x to both sides:

$0.75x{\color{Red} -0.25+0.25}=1.25+0.25$

The red terms cancel out and we add as usual on the right side of the equation.

Now divide both sides by to completely isolate x:

$\frac{{\color{Red} 0.75}x}{{\color{Red} 0.75}}=\frac{1.5}{.75}$

The red terms cancel to 1. The right side is divided as normal. A short cut for dividing decimals is to relate them to coins or convert them to fractions. On the right side we have $1.50 in the numerator and .75 cents in the denominator. It takes two sets of .75 cents to make a $1.50. So x=2.

If this analogy does not work then convert the decimals to fractions. Three divided by two is 1.5 and 3 divided by 4 is .75. When we divide a fraction by a fraction we multiply the numerator by the reciprocal of the denominator. $\frac{3}{2}*\frac{4}{3}=\frac{12}{6}=2$

If either of these methods are not easily applicable to the problem, seem like too much work, or are too abstract, then move the decimal of the divisor to make it a whole number. Then move the decimal of the dividend the same number of decimal places. Now divide as usual.

Using this method on the right side of our equation:

$\frac{{\color{Red} 0.75}x}{{\color{Red} 0.75}}=\frac{1.5}{.75}\rightarrow x=\frac{1.5}{{\color{Blue} 75}}=\frac{{\color{Green} 150}}{75}=2$

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Question

Find the value of in the equation.

Answer

With a two step equation don't forget when solving the problem do the inverse operation. That means opposite of addition is subtraction and vice versa and opposite of multiplication is division and vice versa. Make sure what ever you do to one side you do to the other as well. Tip: Do addition or subtraction first, then multiplication or division.

${\color{Red} - 12 - 12}$

$\frac{6.75x}{{\color{Red}6.75 }} = \frac{81}{{\color{Red}6.75 }}$

Check your answer by substituting x back into the equation. Both sides should equal.

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Question

Solve:

Answer

To isolate the unknown variable, first subtract one from both sides.

Divide by on both sides of the equation.

$\frac{-0.2}{-0.2}x =\frac{-0.8}{-0.2}$

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Question

Solve:

Answer

In order to solve the equation, we have to isolate the variable. We do this by performing the same operation to either side of the equation.

To isolate the unknown variable, first subtract from both sides.

Divide both sides by .

$\frac{0.5x}{0.5} =\frac{-2}{0.5}$

If dividing by a decimal if difficult, multiply the numerator and denominator by ten to get whole integers.

$\frac{-2\cdot 10}{0.5\cdot 10}=\frac{-20}{5}$

Now factor the numerator to find a common factor to cancel out.

$\frac{-20}{5}=\frac{-4\cdot 5}{5}=-4$

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Question

Solve:

Answer

To solve for the unknown variable, first subtract from both sides of the equation.

Divide on both sides.

$\frac{0.5x}{0.5} =\frac{0.95}{0.5}$

If dividing by decimals is difficult, just multiply both decimals by 100 to get integers.

$\frac{0.95\times 100}{0.5\times100} = \frac{95}{50}$

When you multiply by 100 you move the decimal two spaces to the right.

From here factor the numerator and cancel like terms.

$\frac{95}{50}=1.9$

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Question

Solve:

Answer

To isolate the unknown variable, first subtract from both sides.

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Question

Compute:

Answer

In order to solve the equation, we have to isolate the variable. We do this by performing the same operation to either side of the equation.

Subtract from both sides of the equation.

Divide on both sides.

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Question

Solve:

Answer

In order to solve the equation, we have to isolate the variable. We do this by performing the same operation to either side of the equation.

To solve for , combine like-terms by subtracting.

Divide both sides by .

$\frac{-0.1x }{-0.1}= \frac{0.5}{-0.1}$

Decimals may be written as fractions.

$-0.1=-\frac{1}{10}$

$0.5=\frac{1}{2}$

Dividing by a fraction is the same as multiplying by its reciprocal:

Thus we can replace the decimals with their fraction equivalents:

$x=\frac{1}{2}\times -\frac{10}{1}=\frac{-10}{2}=\frac{-5\cdot 2}{2}$

Canceling out the two that is in the numerator and in the denominator we arrive at our final answer.

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Question

Evaluate:

Answer

In order to solve the equation, we have to isolate the variable. We do this by performing the same operation to either side of the equation.

Subtract on both sides of the equation.

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