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Pre-Algebra Ch.3 Multi-Step Equations & Inequalities
by Kim, Jung Woo
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Pre-Algebra Ch.3 Multi-Step Equations & Inequalities

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Lesson 3.1 Solving Two Step Equations

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Example Problem

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Lesson 3.2 Solving Equations Having Like Terms and Parentheses

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Example Problem

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Lesson 3.3 Solving Equations with Variables on Both Sides

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Example Problem

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Lesson 3.4 Solving Inequalities using Addition or Subtraction

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Example Problem

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Example Problem

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Lesson 3.5 Solving Inequalities Using Multiplication or Division

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Example Problem

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Example Problem

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Lesson 3.6 Solving Multi-Step Equations

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Example Problem

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Example Problem

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How to Check Answer

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Example Checking

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New node

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How to check your answer

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To solve Two Step Equations, you will use addition,subtraction, multiplication or division property of equality. We will want the variable to be all by it self. Remember to keep the equal signs lined up so that it is easy to follow the Math.

5x + 9 = -26So I will have to get the variable alone so i will first use the subtraction property of equality to get rid of the 9. so i will have to subtract 9 and subtract 9 from -26 which gives me 5x=-35 now I will use the Division property of equality. I will divide 5x by 5 and -35 by 5 which givesx= -7

To solve equations with like terms and parentheses, you should first combine the like terms.

For example on this problem 4x-2+3x-x+8=-25the like terms are 4x, +3x, and -xSo we will add 4x +3x -x =7x-1x=6xNow we got our 6x and our left overs which are -2 and +8. -2+8 =6. Here we can set up our Two Step Equation.6x+6= -25 We will use the Subtraction Property Of Equality and the Division Property of Equality. See Pic.

The big message of this lesson is to get the Variable to one side.

5n-2=7n+14First we subtract 5n from 5n and5n from 7n which gives us this :-2=2n+14 Now I will subtract 14 for both sides. -2 - 14 and 14 - 14 gives me with -16 = 2n Here we use the Division property of equality to get the variable alone.so 2n/2 and -16/2 which finally givesn= -8

An inequality is a statement formed by placing an inequality symbol between two expressions. the solution of an inequality is a number that you can substitue to a variable

So i have x -6 ≤ -3 so I will get the variable by it self. So i will add 6 to both sides which gives me x ≤ 3

x-6 ≤ -3 Here we will have to get x by itself using the addition property of inequality. So I will add 6 and add to -3 also which gives me x ≤ 3 . Now if we graph this we would have • and an arrow going left because x is smaller or equal to.

When you divide or multiplying by a negative when solving inequalities, your sign reverses

So i have -7x ≥ -35 so I will get the variable to one side. so i will divide both sides by -7 which gives me x ≤ 5 The sign reversed because I multiplied by a negative number

-7x ≥ -35 so i will divide -7 from -7x and also to -35. which will give me x ≤ 5. My sign reversed because I divided by a negative number.

Multi step equations uses every property.

2x + 7 > 4x - 3 I will first get the variable to one side by subtracting 4x from 2x and 4x from 4x which gives-2x + 7 > -3 I will now subtract 7 from both sides giving me -2x < -10 my sign reversed because I divided by a negative numberNow I will divide both numbers by -2 which gives X < 5 The circle is not colored in because it does not include the number 5

2x + 7 > 4x - 3First I will subtract 4x from 4x and 4x from 2x which results-2x + 7 > -3 Now i subtract 7 from +7 and -3 which gives-2x > -10 Now we divide both numbers by -2. Here our sign reverses because i divided by a negative number. which gives x < 5

Checking answer is very important.

All you do is substitue the variable with the answer. Here I got x = -7 so I will plug in -7 to x and will get this equation :5(-7) + 9 = -26-35 + 9 = - 26and it is correct!