Pre-Algebra - Algebraic Equations

Solve:

Explanation

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.

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

Solve for .

Explanation

Divide both sides by . Both decimals each have one decimal place so the expression becomes: $\frac{0.4}{0.2}=\frac{4}{2}$ .

Sarah is building a fence for her dog's square play area. To reduce the cost, she is using her house as 1 side of the play area, meaning she only has to purchase fencing for the other sides. If she needs to fence in 225 meters2 for her dogs, and fencing costs $2.50 per meter of fencing, what will be the cost of fencing in this square play area?

$\small \small $ 112.50$

$\small $ 562.50$

$\small $ 140.63$

$\small $ 45$

$\small $75$

Explanation

The first step is to figure out the perimeter of the square play yard with an area of 225 meters, first using the fomula:

$\small (area) = (base)^2$

Find the square root of both sides to calculate the length of the base of the square

$\small \small \small \small \sqrt225 = (base) = 15$

All the sides are of equivilent length, so the total amount of fence required is:

$\small \small (15)*3 = 45$

One side is "fenced" by the house, so that fenching does not need to be paid for. Thus, only the remaining 3 sides need to be paid for.

Finally, multiply the length of fencing needs by the cost of fence per foot to find your answer:

$\small 45 * $2.50 = $112.50$

Solve for .

$\frac{x}{-0.9}=-3.1$

Explanation

$\frac{x}{-0.9}=-3.1$ Multiply both sides by . When multiplying decimals, first multiply normally and then count the number of decimal places in the problem. We have . So starting from the right, we shift two places to the left to get a decimal of . Since we are multiplying with negative numbers, we need to determine if the answer is negative. There are two negative numbers and that means the answer is positive.

Evaluate:

Explanation

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,

Solve:

Explanation

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.

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

Solve:

$\frac{1}{4}$

Explanation

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,

Solve:

$\frac{1}{4}$

Explanation

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,

Solve for .

Explanation

Divide both sides by . Both decimals each have one decimal place so the expression becomes: $\frac{0.4}{0.2}=\frac{4}{2}$ .

Solve for .

Explanation

Divide both sides by . Both decimals each have one decimal place so the expression becomes: $\frac{1.5}{0.3}=\frac{15}{3}$ .

Algebraic Equations

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