Sumner Solving Equations

One-step equations

100

Solve for x. x + 2 = 5

What is 3? x + 2 = 5 -2 -2 x = 3

200

13x = 26

What is 2? 13x = 26 divide 13 on both sides 13 divided by 26 = 2

300

Solve for x. x/4 = 12

What is 48? Since x is divided by 4, we must do the opposite and multiply both sides by 4. 12 x 4 = 48

400

Solve for y. y + 10 = 3

What is -7? y + 10 = 3 - 10 -10 y = -7

500

Solve for z. -3z = 39

What is -13? Since z is being multiplied by -3, we must do the opposite and divide each side by -3. 39 divided by -3 = -13

Two Step Equations

100

Solve for x. 2x + 4 = 6

What is 1? 2x + 4 = 6 - 4 -4 2x = 2 Divide each side by 2. 2 divided by 2 = 1.

200

Solve for x. 7x + 3 = 31

What is 4? 7x + 3 = 31 - 3 - 3 7x = 28 Since x is being multiplied by 7, you must divide each side by 7. 28 divided by 7 = 4

300

Solve for z. -3z - 7 = 23

What is -10? -3z - 7 = 23 +7 +7 -3z = 30 Since z is being multiplied by -3, you must divide each side by -3. 30 divided by -3 = -10

400

Solve for x. 11 - 7x = 18

What is -1? 11 - 7x = 18 -11 -11 -7x = 7 Since x is being multiplied by -7, we must divide each side by -7. 7 divided by -7 = -1.

500

Solve for x. -6 + x/3 = 3

What is 27? -6 + x/3 = 3 +6 +6 x/3 = 9 Since x is being divided by 3, we must multiply each side by 3. 9 x 3 = 27

Combining Like Terms

100

Simplify: 4x + 2x + 13 - 25

6x - 12

200

Simplify: 9x - 7x - 5 + 17 + 6y

2x + 6y + 12

300

Simplify: 7(w - 3) + 4y -16

7w - 21 + 4y - 16

7w + 4y -37

400

Simplify: -4(a + 5) - 3a - 27

-7a - 47

500

Simplify: 6m - 7p - 4m - 16 -23p

2m -30p -16

Using Distributive Property

100

Solve for x. 3(x + 2) = 12

What is 2? First you must apply the distributive property by multiplying 3 to every term in the parenthesis. 3x x = 3x and 3 x 2 = 6. New equation is 3x + 6 = 12 - 6 -6 3x = 6 Since x is being multiplied by 3, we must divide both sides 3. 6 divided by 3 = 2

200

Solve for w. 5(w - 3) = 45

What is 12? First we must apply the distributive property by multiplying 5 by each term in the parenthesis. 5 x w = 5w. 5 x -3 = - 15. New equation: 5w - 15 = 45 +15 +15 5w = 60 Since w is being multiplied by 5, you must divide each side by 5. 60 divided by 5 = 12.

300

Solve for w. 5(2w - 7) = 65

What is 10? First, you must apply the distributive method by multiplying 5 by each of the terms in the parethesis. 5 x 2w = 10w and 5 x -7 = -35 New equation: 10w - 35 = 65 +35 +35 10w = 100 Since w is being multiplied 10, we must divide each side by 10. 100 divided by 10 = 10.

400

Solve for y.     -6(y + 4) = 30

y = -9

500

Solve for w.     -5(w - 3) = 18

w = -3/5

Vocabulary

100

A letter that represents a number in an equation. Hint: It is the "x" in the following equation: x + 1 = 2

What is a variable?

200

A number all by itself in an equation Hint: It is the 1 and 2 in the following equation. x + 1 = 2

What is a constant?

300

It is the number that is multiplied by a variable in an equation. Hint: It is the 4 in the following equation: 4a = 16

What is a coefficient?

400

A mathematical phrase that contains numbers, variables, and operations, but NO equal sign

expression

500

A mathematical sentence that contains numbers, variables, operations and an equal sign

Equation