Chapter 3: Multi-Step Equations and Inequalities by S S

Chapter 3: Multi-Step Equations and Inequalities

3.4: Solving inequalities using Addition or Subtraction

Vocabulary

Inequality: A mathematical symbol formed by placing an inequality symbol between the two expressions.For example greater than, less than, greater or equal to, or less than or equal to. Solution of an inequality: The set of all numbers that produce true statements when substituted for the variable in the equation.

Examples:

Example 1: m+5>=10   Write original equation m+5-5>=10-5   Subtract 5 from each side m>=5 Example 2: -10>x-12      Write the original eqution -10+12>x-12+12   Add 12 to each side 2>x                      Simplify

3.3: Solving equations with variables on both Sides

Note:

Try to put the variable on one side of the equation!

Example:

Example 1: 7n-5=10n+13    Write original equation 7n-5-7n=10n+13-7n   Subtract 7n from each side -5=3n+13  Simplify -5-13=3n+13-13     Subtract13 from each side -18=3n    Simplify -18/3=3n/3   Divide each side by 3 -6=n     Simplify

3.1: Solving Two-Step Equations

Examples:

Example 1: 3x + 7= -5               Write original equation. 3x + 7-7 = -5 -7      Subtract 7 from each side 3x=-12                     Simplify 3x/3=-12/3            Divide each side by 3 x=-4                 Simplify   Example 2: 7-4y=19      Write th original equation 7-4y-7=19-7  Subtract 7 from each side -4y=12         Simplify -4y/-4=12/-4  Divide each side by -4 y=-3            Simplify              

Definition

Two step Equations are simply equations that are solved in two steps trying to solve for the variable, using addition property of equality, subtraction property of  equality, division property of equality , and multiplication property of equality.

3.2: Solving equations having like terms and parenthesis

Examples :

Example 1: 5.20n+0.80n+47=377    Substitute 6.00n+47=377            Combine like terms 6n+47-47=377-47     Subtract 47 from each side 6n=330                     Simplify 6n/6=330/6                dive each side by six n=55 Example 2: -21=7(3-x)=12       Write original equation -21=21-7x              Distributive property -21-21=21-7x-21     Subtract 21 from each side -42=-7x                  Simplify -42/-7=-7/-7             Divide seven from each side x=3                         Simplify

3.5: Solving inequalities using Multiplication and Division

Examples

Example 1: m/-3>3      Write original inequality -3 *m/-3 m Example 2: -10t>=34 Original inequality -10t/-10 t

3.6: Solving multi-step equations

Examples:

Example1: 88+10g>138     Substitute 88+10g-88>138-88   Subtract 88 from each side 10g>50    Simplify 10g/10>50/10   Divide each side by  10 g>5  simplify Example 2: x/-4-6>=-5  Original inequality x/-4-6+6>=-5+6  Add six to each side x/-4>=1 Simplify -4*x/-4 x