Objective translate verbal sentences into equations

Section 2.4, “Variables and Equations” mathematical sentence formed by placing an “=“ between two expressions y – 8 = 12 22 = 14 + z x ÷ 5 = 30 11a = 121

Equation x + 7 = 10 Left side Right side ‘x’ has to be 3 in order to make the equation balanced. Like a scale, the left side and right side must be the same in order to be balanced!

Writing Algebraic Expressions Operation Verbal Phrase Expression Addition Sum, plus, total, more than, increased by 5 + n k + 12 Subtraction Difference, less than, minus, decreased by 12 – p x – 12 Multiplication Product, times, of, multiplied by 3 x 5 3(d) (n)(w) p ∙ k Division Quotient, divided by, divided into k/7 14 ÷ r Writing Equations Symbol Meaning Key phrases = Is equal to The same as, is

Translate verbal phrases into equations the difference of a number k and 8 is 12. k – 8 = 12 6n = 24 b. the product of 6 and a number n is 24. y + 5 = 13 c. the sum of a number y and 5 is 13. z ÷ 2 = 7 d. the quotient of a number z and 2 is 7.

A SOLUTION of an equation with a variable is a number that produces a TRUE statement when it is substituted for the variable. Tell whether 19 or 20 is a solution to the equation. k – 8 = 12 (19) – 8 = 12 (20) – 8 = 12 11 ≠ 12 12 = 12 19 is NOT A SOLUTION 20 is a SOLUTION

SOLUTION– (9) – 2 = 6 k – 2 = 6 7 ≠ 6 54 = 54 6n = 54 6(9) = 54 when you substitute for a variable the solution can be either TRUE or FALSE. Substitute 9 for each variable. Is 9 the solution for each equation? (9) – 2 = 6 k – 2 = 6 NOT A SOLUTION 7 ≠ 6 6n = 54 6(9) = 54 SOLUTION 54 = 54 SOLUTION 4 = 36/s 4 = 36/(9) 4 = 4

x + 8 = 12 16 – m = 2 20 = 5y v ÷ 8 = 8 Mental Math When solving simple equations using mental math, think of the equation as a question. x + 8 = 12 “What number plus 8 is equal to 12? “ x = 4 16 – m = 2 “16 minus what number is equal to 2? “ m = 14 20 = 5y “20 is equal to 5 times what number? “ y = 4 v ÷ 8 = 8 “What number divided by 8 is equal to 8? “ v = 64

Objective solve equations using addition and subtraction In your notebook, draw a picture of what an equation looks like to you. Explain why your picture is “like an equation.” Then use your picture to solve an equation of your own.

EQUATION – y – 8 = 12 22 = 14 + z 5 ÷ x = 30 11a = 121 mathematical sentence formed by placing an “=“ between two expressions y – 8 = 12 22 = 14 + z 5 ÷ x = 30 11a = 121

Equation x + 7 = 10 Left side Right side ‘x’ has to be 3 in order to make the equation balanced. Like a scale, the left side and right side must be the same in order to be balanced!

Section 2.5 “Solving Equations Using Addition & Subtraction” How can you get the “unknown” by itself? m + 24 = -18 “Undo” the operation by using the INVERSE (opposite) operation to both sides of the equation.

Solving Addition Equations… Isolate the variable! Get ‘m’ by itself. m + 24 = -18 To get the ‘m’ by itself get rid of “adding 24.” –24 – 24 Do the opposite. “Subtract 24.” m = -42 Whatever you do to one side of the equation you must do the other side. -18 – 24 -18 + (-24) “opp-opp” -42

m = -42 m + 24 = -18 (-42) + 24 = -18 -18 = -18 Check Your Work! -18 = -18 Are both sides equal?

Try It Out 1). (6) + 7 = 13 1). x + 7 = 13 2). -7 = 9 +(-16) 1). (6) + 7 = 13 2). -7 = 9 +(-16) 3). -3 = (-14) + 7 + 4 4).(3.5) – 0.4 = 3.1 1). x + 7 = 13 2). -7 = 9 + h 3). -3 = x + 7 + 4 4). f – 0.4 = 3.1

Solving Subtraction Equations… Isolate the variable! Get ‘y’ by itself. -13 = y –15 To get the ‘y’ by itself get rid of “subtracting 15.” +15 +15 Do the opposite. “Add 15.” 2 = y Whatever you do to one side of the equation you must do the other side.

2 = y -13 = y – 15 -13 = (2) – 15 -13 = -13 Check Your Work! Are both sides equal?

Try It Out 1). (4) - 7 = -3 1). t - 7 = -3 2). 6 = -3 + (9) 3). ¾ = (3¼)– 2½ 4). -1.5 = (5.5) - 7 1). t - 7 = -3 2). 6 = -3 + x 3). ¾ = r – 2½ 4). -1.5 = p - 7