Equations

What is an equation?Has an equal sign (=) It can be solvedIt is balanced.

Has variables,constants, coefficients, operations and sometimes parenthesis.

A solved equation has a standard form

• Standard form of a solved equation is:

• Number of steps to solve an equation and bring it to standard form:• It can take just one step to solve an equation• Two- steps to solve an equation • Multi-steps to solve an equation and reduce it to its standard form• Variable = constant.

Variable = constantX = 5

Solve a one-step linear equation(with no exponents)

Example: Solve 1. X + 5 = 10 Left Right

Step one : First draw a border/line between both sides of the equal sign and label as left side and right side. X + 5 = 10 Step Two: Identify if the equation is in its standard form

Step two : If “NO” Isolate the variable/Alphabet to the left sideAnd move all the constants to right side. X + 5 = 10 - 5 -5 X = + 5

Step four: Now check again if it is in the standard form : If “yes” you have found your solution/solved your equation. IF “NO” repeat these steps until you get to the standard form.

YES NO

Example two (TWO-STEP)

• 2X + 5 – X = 15 left right• Step 1: Draw a line to separate the sides +2X + 5 – X = 15

• Step 2: Identify if the equation is in standard form? If “NO” isolate the variable/combine like terms if terms are on the same side.

Left right

• 2X + 5 – X = 15; The variable’s X are on the same side so combine. • 1X + 5 = 15; Now is it in standard form? If “No” isolate the variable

and move the + 5 to the right side 1X + 5 = +15 - 5 = -5 1X = +10

Example 3(Simple multi-step)• 4X + 6 + 2X = 24 ; left right

• Step 1: Draw lines to separate the sides. 4X + 6 + 2X = 24• Step 2: Check if it is in the standard form? “yes” or “ No” ; If No then Isolate

the variable/ combine like terms if on the same side.• left right• +4X + 6 + 2X = 24 ; combine 4x + 2x

• +6x + 6 = 24 ; check to see if in the standard form- “NO” repeat step 2(isolate the variable).

+ 6X + 6 = + 24 - 6 = -6+ 6X = + 18 Check if in standard form; “NO” then use multiplicative inverse

Continued…

• + 6X = + 18 use multiplicative inverse property to get rid of the co-efficient • The multiplicative inverse of 6 is 1 6 1 . 6X = + 18 1 ; 6X = 18 = Check if in 6 6 6 6Check if in standard form (variable = constant); if “ yes” you have solved the equation/found the solution for X.

1 X = 3