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Pre-Algebra : Algebraic Equations

Study concepts, example questions & explanations for Pre-Algebra

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Example Questions

Example Question #4 : Two Step Equations With Decimals

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

Possible Answers:

x = 2.1875

x = 1.1875

x = 18.88

x = 22.4

x= 12.16

Correct answer:

x = 22.4

Explanation:

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

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

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

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

x = 22.4

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Example Question #5 : Two Step Equations With Decimals

Solve for :

2.4x - 1.2 = 8.1

Possible Answers:

x = 4.575

x = 3.875

x = 22.32

x = 2.875

x = 16.56

Correct answer:

x = 3.875

Explanation:

2.4x - 1.2 = 8.1

2.4x - 1.2+ 1.2 = 8.1 + 1.2

2.4x = 9.3

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

x = 3.875

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Example Question #2 : Two Step Equations With Decimals

Solve for :

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

Possible Answers:

x= 1.525

x = 37.12

x = 30.4

x = 33.6

x= 4.725

Correct answer:

x = 33.6

Explanation:

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

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

x - 1.6 = 32

x - 1.6 + 1.6 = 32 + 1.6

x = 33.6

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Example Question #2 : Two Step Equations With Decimals

Solve for .

.1x+.9=2

Possible Answers:

x=20

x=10

x=.1

x=1.9

x=11

Correct answer:

x=11

Explanation:

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

.1x=2-.9

.1x=1.1

x=11

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Example Question #3 : Two Step Equations With Decimals

Solve for :

0.75x+0.25=4.75

Possible Answers:

6.25

5.75

Correct answer:

Explanation:

Explanation:

Step 1: Subtract 0.25 from both sides:

0.75x+0.25-0.25=4.75-0.25

0.75x+0=4.5

0.75x=4.5

Step 2: Divide both sides by 0.75 :

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

x=6

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Example Question #3 : Two Step Equations With Decimals

Solve the equation for .

0.9 + x = 2x - 0.7

Possible Answers:

x = 0.2

x = 0.4

x = -0.16

x = 0.32

x = 1.6

Correct answer:

x = 1.6

Explanation:

The correct answer to this question is x = 1.6 .

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:

0.9 + x-x = 2x - 0.7-x

0.9 = x - 0.7

Next, you add 0.7 to the left side of the equation to put all of the numbers on the same side of the equation:

0.9+0.7 = x - 0.7+0.7

0.9+0.7 = x

Once you do this, you can add the numbers on the left side of the equation together and find that x = 1.6 .

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Example Question #5 : Two Step Equations With Decimals

Solve for x: 0.2x+99.4 = 108.9

Possible Answers:

x=47.5

x=41.66

x=1,041.5

x=4.75

x=1.9

Correct answer:

x=47.5

Explanation:

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:

0.2x+99.4 = 108.9 right now it says to add 99.4 , so we'll subtract it from both sides.

0.2x = 9.5 next we will do multiplication/dividion. Right now it is multiplying by 0.2 , so we will divide both sides by 0.2 .

x=47.5

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Example Question #101 : Two Step Equations

Solve for :

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

Possible Answers:

6.4

9.2

5.62

Correct answer:

Explanation:

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

Use distributive property, multiply 1.2 and 6.4

7.68y = 69.12

Divide both sides by 7.68

y=9

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Example Question #12 : Two Step Equations With Decimals

Solve: -0.2x+1 = 0.2

Possible Answers:

0.6

0.16

Correct answer:

Explanation:

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

-0.2x+1 -(1)= 0.2-(1)

-0.2x =-0.8

Divide by -0.2 on both sides of the equation.

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

x=4

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Example Question #11 : Two Step Equations With Decimals

Solve for :

0.75x-0.25=1.25

Possible Answers:

x=1.33333

x=2.33333

x=2

x=1

None of the other answers.

Correct answer:

x=2

Explanation:

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.

0.75x-0.25=1.25

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.

0.75x=1.50

Now divide both sides by 0.75 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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Pre-Algebra : Algebraic Equations

Study concepts, example questions & explanations for Pre-Algebra

All Pre-Algebra Resources

Example Questions

Example Question #4 : Two Step Equations With Decimals

Example Question #5 : Two Step Equations With Decimals

Example Question #2 : Two Step Equations With Decimals

Example Question #2 : Two Step Equations With Decimals

Example Question #3 : Two Step Equations With Decimals

Example Question #3 : Two Step Equations With Decimals

Example Question #5 : Two Step Equations With Decimals

Example Question #101 : Two Step Equations

Example Question #12 : Two Step Equations With Decimals

Example Question #11 : Two Step Equations With Decimals

All Pre-Algebra Resources

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