Two-Step Equations with Decimals - Pre-Algebra

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Solve for p:

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

Solve for :

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Step 1: Subtract from both sides:

Step 2: Divide both sides by :

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

Solve for :

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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}$$

Solve for .

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

Solve for :

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Explanation:

Step 1: Subtract from both sides:

Step 2: Divide both sides by :

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

Solve the equation for .

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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 .

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

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$$\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$

Solve for :

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

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

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

Solve for :

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

Solve for :

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

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

Use distributive property, multiply and

Divide both sides by

Solve for x:

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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 .

Solve for :

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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:

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

Find the value of in the equation.

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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.

Solve:

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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}$

Solve:

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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$

Solve:

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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}$=1.9$

Solve:

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

Compute:

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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.

Solve:

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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.

Evaluate:

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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.