Two-Step Equations - Pre-Algebra

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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.

Subtract on both sides of the equation.

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Question

Solve:

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Answer

Subtract from both sides of the equation.

Divide by two on both sides.

$\frac{2x}{2}=\frac{0.18}{2}$

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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.

First, square the decimal.

Subtract this value from both sides to isolate the unknown variable.

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Question

Solve:

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Answer

To solve for , first add 1.5 on both sides of the equation.

Divide both sides by negative three.

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Question

Solve:

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Answer

In order to solve this equation, first add on both sides of the equation.

Simplify the left and right side of the equation.

Convert the decimal on the left side of the equation to a fraction.

$0.2 = \frac{1}{5}$

Rewrite the equation.

$\frac{1}{5}x=1$

To isolate the unknown variable, multiply by the reciprocal of $\frac{1}{5}$ , or , on each side of the equation.

$\frac{1}{5}x \times 5=1\times 5$

Simplify the left and the right side of the equation.

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Question

Solve:

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Answer

In order to solve this equation, we need to group the terms and separate the integer .

Add on both sides.

Add both sides by .

Add the left side of the equation to get .

The answer is:

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Question

Solve the following equation:

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Answer

To isolate the variable, subtract nine from both sides of the equation.

Simplify both sides of the equation.

Convert the decimal on the left side of the equation to a fraction.

$0.9 = \frac{9}{10}$

Rewrite the equation.

$\frac{9}{10}x= 10$

Multiply both sides by $\frac{10}{9}$ to get by itself.

$\frac{9}{10}x \times \frac{10}{9}= 10 \times \frac{10}{9}$

Simplify both sides of the equation. Multiply the tens together on the right side of the equation and leave the fraction in improper form.

The answer is: $x= \frac{100}{9}$

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Question

Solve the two-step equation below.

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Answer

Use properties of equality. Start with either subtraction or addition then multiplication or division.

Now divide by 32.

$\frac{32x}{32} = \frac{232}{32}$

Check your answer by substituting 7.25 in place of x.

Both sides are equal.

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Question

Find the solution for y.

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Answer

In this two step equation we must isolate and find the solution of y. So the first step is to add both sides by 3.4 as follows:

The next step is divide both sides by 1.25 as follows:

$\frac{1.25}{1.25}y=\frac{10.0}{1.25}\Rightarrow y =\frac{10.0}{1.25}=8$

You can check your answer by inserting 8 into y in the original equation as follows:

$1.25(8)-3.4=6.6\Rightarrow 10.0-3.4=6.6\Rightarrow 6.6=6.6$

It's correct!

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Question

Solve for :

$\frac{2}{3}s+\frac{1}{3}=-\frac{1}{3}$

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Answer

$\frac{2}{3}s+\frac{1}{3}=-\frac{1}{3}$

$\frac{2}{3}s+\frac{1}{3}-\frac{1}{3}=-\frac{1}{3}-\frac{1}{3}$

$\frac{2}{3}s=-\frac{2}{3}$

$\frac{3}{2}\cdot \left(\frac{2}{3}s\right)=\frac{3}{2}\cdot \left(-\frac{2}{3}\right)$

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Question

Solve for :

$\frac{2}{3}x-\frac{1}{4}=\frac{1}{6}$

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Answer

Step 1: Add $\frac{1}{4}$ to both sides:

$\frac{2}{3}x-\frac{1}{4}+\frac{1}{4}=\frac{1}{6}+\frac{1}{4}$

$\frac{2}{3}x+0=\frac{1}{6}+\frac{1}{4}$

$\frac{2}{3}x=\frac{1}{6}+\frac{1}{4}$

Step 2: Add $\frac{1}{6}$ to $\frac{1}{4}$ . Remember that when you add fractions, you must find common denominator. The common denominator for $\frac{1}{4}$ and $\frac{1}{6}$ is . $\frac{1}{6}$ becomes $\frac{2}{12}$ when you multiply both the numerator and the denominator by . Similarly, $\frac{1}{4}$ becomes $\frac{3}{12}$ when you multiply both the numerator and the denominator by .

$\frac{2}{3}x=\frac{1}{6}+\frac{1}{4}$

$\frac{2}{3}x=\frac{2}{12}+\frac{3}{12}$

$\frac{2}{3}x=\frac{5}{12}$

Step 3: Multiply both sides of the equation by the reciprocal of $\frac{2}{3}$ :

$\frac{3}{2}\times \frac{2}{3}x=\frac{5}{12}\times \frac{3}{2}$

$1x=\frac{15}{24}$

$x=\frac{15}{24}$

Step 4: Simplify the fraction by dividing the numerator and the denominator by the Greatest Common Factor (GCF). The GCF of and is :

$x=\frac{15}{24}=\frac{\frac{15}{3}}{\frac{24}{3}}=\frac{5}{8}$

$x=\frac{5}{8}$

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Question

Solve for p:

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Answer

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

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Question

Solve for :

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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 :

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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 .

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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 :

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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 .

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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

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

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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 :

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

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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 :

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Answer

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

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