Algebraic Equations - Pre-Algebra

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Question

Solve the equation for x. Give your answer to three decimal places.

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Answer

Solve by isolating x on one side of the equation and collecting the decimal terms without variables on the other.

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Question

Solve.

$10.8\times 22.3= ?$

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Answer

Multiply the numbers as you would any three-digit numbers, ignoring the decimal points. After adding the three lines together, place the decimal point however many spots from the right as there are decimal points moved from the right in the original equation. Because both 10.8 and 22.3 have decimals one over from the right of the number, totaling two decimals over, you will move the decimal over two decimal places in the final solution.

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Question

Solve for :

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Answer

To solve for "x" means to get x by itself on one side of the equation.

To isolate x we perform the opposite mathematical operation that the equation calls for. This ensures that we cancel out one term which is needed to move towards our goal of getting x by itself.

Add to both sides:

$x{\color{Red} -0.27+0.27}=0.43 +0.27$

The red terms cancel each other out and the right side is added as usual. The simplest way to add or subtract decimals is to align the decimal points and perform the indicated mathematical operation as you would with whole numbers.

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Question

Solve:

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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.

Therefore, divide both sides by to solve for the unknown variable.

$\frac{0.2x }{0.2}= \frac{10}{0.2}=50$

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Question

Solve:

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Answer

To solve this equation, we will need to isolate the unknown variable. Subtract on both sides of the equation.

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Question

Evaluate:

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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 , divide both sides by .

$\frac{0.06x}{0.06} = \frac{3}{0.06}$

If dividing by decimals is difficult, multiply the numerator and denominator by 100 to get whole numbers to divide.

$\frac{3\cdot 100}{0.06\cdot 100}=\frac{300}{6}$

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

$=\frac{300}{6}=\frac{6\cdot 50}{6}=50$

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Question

Solve:

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Answer

To determine the value of the unknown variable, isolate the term by dividing both sides by .

$\frac{1.04x}{1.04} = \frac{-3.12}{1.04}$

If dividing by decimals is difficult, you can convert each decimal into an integer by multiplying each number by 100 or moving the decimal to the right two places.

$\1.04\times 100 x=-3.12\times 100\ 104x=-312$

Now divide,

$\frac{104x}{104}=\frac{-312}{104}=\frac{-3\cdot 104}{104}=-3$

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Question

Solve:

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Answer

To solve for the unknown variable, divide both sides by .

$\frac{0.33x }{0.33}= \frac{66}{0.33}$

If dividing by decimals is difficult, you can convert the decimal into an integer by multiplying the decimal number by 100 or moving the decimal to the right two places.

${0.33x \times 100 }= 66 \times 100$

Now divide each side by 33 and then factor the numerator to simplify the fraction.

$\frac{33x}{33}=\frac{6600}{33}$

$x=\frac{200\cdot 33}{33}=200$

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Question

Solve:

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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 , divide both sides by .

$\frac{0.04x }{0.04}= \frac{0.8}{0.04}$

$\frac{0.8}{0.04} = \frac{80}{4}$

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

$\frac{0.8\times 100}{0.04\times100} = \frac{80}{4}$

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

From here factor the numerator and cancel like terms.

$\frac{80}{4}=\frac{20\cdot 4}{4}=20$

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Question

Solve:

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Answer

Divide on both sides of the equation.

$\frac{0.15x}{0.15} = \frac{15}{0.15}$

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Question

Solve:

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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 to isolate the .

Add a placeholder if necessary.

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Question

Solve:

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Answer

In order to solve for , subtract from both sides.

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Question

Solve:

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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.

Divide both sides by to isolate the variable.

$\frac{0.1x }{0.1}= \frac{1000}{0.1}$

Decimals may be written as fractions.

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

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

$\frac{1000}{1}\times \frac{10}{1}$

Therefore,

.

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Question

Solve:

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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.

Divide on both sides to isolate the unknown variable.

$\frac{0.003x}{0.003} = \frac{3.3}{0.003}$

Decimals may be written as fractions.

$0.003=\frac{3}{1000}$

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

$3.3\times \frac{1000}{3}$

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Question

Solve:

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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 , divide both sides by

$\frac{0.6x }{0.6}= \frac{24}{0.6}$

Decimals may be written as fractions.

$0.6=\frac{6}{10}$

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

Substitute and solve.

$x=\frac{24}{1}\times\frac{10}{6}$

$x=\frac{240}{6}=\frac{6\cdot 40}{6}$

The six in the numerator and in the denominator cancel out and we are left with the final answer,

.

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Question

Solve:

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Answer

To isolate the unknown variable, subtract on both sides of the equation.

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Question

Solve for :

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Answer

Isolate the variable by dividing both sides by .

$\frac{0.2}{0.2}x = \frac{0.3}{0.2}$

The fraction can be solved by moving the decimal on both the denominator and numerator one unit to the right.

The answer is: $\frac{3}{2}$

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Question

Solve and express the answer as a fraction:

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Answer

To solve for the unknown variable, divide both sides by .

$\frac{0.9x}{0.9} = \frac{8}{0.9}$

Converting to a fraction will become $\frac{9}{10}$ .

When eight divides by this fraction, it is similar to multiplying its reciprocal.

$\frac{8}{0.9} = 8\times \frac{10}{9} = \frac{80}{9}$

The answer is: $\frac{80}{9}$

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Question

Solve:

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Answer

Divide on both sides of the equation to isolate the unknown variable.

$\frac{1.25x}{1.25} = \frac{5}{1.25}$

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Question

Evaluate:

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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.

Solve by dividing on both sides of the equation. Move the decimal two places to the right.

$\frac{0.09x}{0.09} = \frac{27}{0.09} =\frac{2700}{9}$

Now factor the numerator to find values that can cancel out.

$\frac{2700}{9}=\frac{9\cdot 300}{9}$

The nine in the numerator and denominator reduce to one and we are left with our final answer,

.

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