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Pre-Algebra Ch.3 Multi-Step Equations & Inequalities by Mind Map: Pre-Algebra Ch.3 Multi-Step Equations & Inequalities
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Pre-Algebra Ch.3 Multi-Step Equations & Inequalities

Lesson 3.1 Solving Two Step Equations

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.

Example Problem

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

Lesson 3.2 Solving Equations Having Like Terms and Parentheses

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

Example Problem

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.

Lesson 3.3 Solving Equations with Variables on Both Sides

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

Example Problem

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

Lesson 3.4 Solving Inequalities using Addition or Subtraction

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

Example Problem

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

Example Problem

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.

Lesson 3.5 Solving Inequalities Using Multiplication or Division

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

Example Problem

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

Example Problem

-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.

Lesson 3.6 Solving Multi-Step Equations

Multi step equations uses every property.

Example Problem

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

Example Problem

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

How to Check Answer

Checking answer is very important.

Example Checking

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!

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How to check your answer