New Jersey Curriculum Standards 4.1 B 4.3 A, B, C 4.5 A, B, C, D

Objective Solve equations by using addition and subtraction. Solve equations by using multiplication and division.

Glossary Terms Addition Property of Equality Subtraction Property of Equality Division Property of Equality Multiplication Property of Equality

List the Order of Operations Addition/Subtraction Multiplication/Division Exponent Parenthesis Parenthesis Exponent Multiplication/Division Addition/Subtraction In Order to solve for a given variable, turn Order of Operations upside down.

Example No. 1 x + 7 12 = Because 7 is added to x, to find the value of x, subtract 7 -7 -7 x 5 = Whatever is done to one side of the = sign, must be done to the other side. Solving equations is a balancing act.

Example 2 No. 2 x - 2 -8 = Because 2 is subtracted from x, to find the value of x, add 2 +2 +2 x -6 = Whatever is done to one side of the = sign, must be done to the other side.

Example No. 3 a + b c = Because b is added to a, to find the value of b, subtract a -a -a b c - a = Whatever is done to one side of the = sign, must be done to the other side. Solving equations is a balancing act.

Example 4 No. 4 -a + b -c = Because a is subtracted from b, to find the value of b, add a +a +a b -c + a = Whatever is done to one side of the = sign, must be done to the other side.

Solve by keeping them balanced. Do These Together Solve by keeping them balanced. 5. 6. 7 + x = 1 -7 + x = -18 -7 -7 + 7 +7 x = -11 x = -6

Solve by keeping them balanced. Do These Together Solve by keeping them balanced. 7. 8. -w + y = -z w + y = z -y -y + w +w w = z - y y = -z + w

Solve by keeping them balanced. TRY THESE Solve by keeping them balanced. 9. 10. X – 12 = -4 -3 = x + 5 -5 -5 + 12 +12 -8 = x X = 8

Solve by keeping them balanced. TRY THESE Solve by keeping them balanced. 11. 12 x + 5 = 0 X – 6 = 6 -5 -5 + 6 + 6 x = -5 X = 12

Solve by keeping them balanced. TRY THESE Solve by keeping them balanced. 13. 14. -y + n = t a - n = t + n + n + y + y a = t + n n = t + y

Example 5 No. 15 Solve for the given variable 9x = 72 Keep the equation balanced. The relationship between the coefficient 9 and the variable x is multiplication. To solve for x, divide by the coefficient. ÷9 ÷9 x = 8

Example 6 No. 16 Solve for the given variable Keep the equation balanced. X = 0.2 *(11) (11)* 11 The relationship between the 11 and the variable x is division. To solve for x, multiply by the reciprocal. x = 2.2

Do These Together x = -0.8 -6x = 42 4* *4 4 ÷-6 ÷ -6 x = -7 x = -3.2 20. Do These Together 21. -6x = 42 4* x = -0.8 *4 4 ÷-6 ÷ -6 x = -7 x = -3.2

Do These Together x = Z V = I * R Y * * Y Y ÷I ÷ I V = R x = Z Y I 22. Do These Together Solve for R 23. V = I * R Y * x = Z * Y Y ÷I ÷ I V = R x = Z Y I ÷Z ÷ Z x = Y Z

TRY THESE 15 = -3b 1.5* 3 = m *1.5 1.5 ÷-3 ÷ -3 -5 = b 4.5 = m 20.3 21.3 15 = -3b 1.5* 3 = m *1.5 1.5 ÷-3 ÷ -3 -5 = b 4.5 = m

Divide each side of the equal sign by 5. a = 1080 The sum of the interior angles of a regular pentagon is 5400. What is the measure of each angle? Skill 22 Write an equation to describe the problem. 5a = 5400 ÷5 ÷5 Divide each side of the equal sign by 5. a = 1080

In baseball, to compute batting average, use the following formula. 22.2 In baseball, to compute batting average, use the following formula. Hits = Average At Bats Tina has been at bat 80 times and has a batting average of .3125. How many hits did she get? Multiply by 80. 80 * Hits =.3125 * 80 80 Hits = 25

22.3 TRY THESE 22.4 1/6 of an apple pie contains 18 grams of fat. How many grams of fat in the entire pie? Write an equation to describe the situation and solve for the variable. An 8 foot board costs $3.28. How much does each foot cost? Write an equation to describe the situation and solve for the variable. 6* *6 8x = $3.28 8 8 x = 108 x = .41