1 step equations
2-step equations
Draw Solutions on a Number Line
Word Problems
Inequalities
100
Show all work: x + 4 = 10
What is

x+4 - 4= 10 - 4

x = 6

100
Solve. Show all work. 8x - 7 = 17
What is

8x-7+7=17+7

8/8x=24/8

x=3

100
x < -4

Make sure to clearly mark where your circle is on the number line and which direction you are shading

The solution has an open circle at -4 and is shaded to the left.
100
#23 The sum of the page numbers of two facing pages in a book is 145. What are the page numbers?
Two facing pages are 2 numbers right after each other like 2 and 3. So if we say the first page number is x, the second page number is x+1. When we add the page numbers together it is equal to 145.

x + (x+1) = 145

2x+1 - 1= 145 - 1

2/2 x = 144/2

x=72, so the pages are 72 and 73

100
#11 Solve. Show all work. Graph each solution set .

4x - 3 > 1

4x - 3+3 > 1+3

4x > 4

4/4x >4/4

x >1

The number line has an open circle at 1 and is shaded to the right.

200
Solve. Show all work: x - ⅔ = 4
What is

x - ⅔ = 4

x - ⅔ + ⅔ = 4 + ⅔

x = 4 ⅔

200
#2 Solve. Show all work.

4 - 6x = 8

4-4 - 6x = 8-4

- 6/-6 x = 4/-6

x = -4/6 = -2/3

200
x > 10

Make sure to clearly mark where your circle is on the number line and which direction you are shading

The solution has a solid circle at 10 and is shaded to the right.
200
#25 The sum of the interior angle measures of a quadrilateral is 360. The measure of angle A is three times the measure of angle D. The measure of angle B is four times that of angle D. The measure of angle C is 24 more than angle B. Find the measure of each angle of the quadrilateral.

The facts from annotating the problem are: angle D=x, angle A = 3x, angle B=4x, and angle C=24.

x+ 3x+4x+24 = 360

8x + 24 = 360 Add like terms

8x + 24 - 24 = 360 - 24 Inverse addition and DSBS

8/8 x = 336/8 Inverse * and DSBS

x = 42, so angle D = 42, Angle A=3*42=126, Angle B=4*42=168

checking: 42+126+168+24=360

200
#12 Solve. Show all work. Graph the solution set.

6 < 1 - 5x

6 -1< 1-1 - 5x

5< - 5x

5/-5< -5/-5x

-1 > x

OR x < -1

(The symbol switches because you are * or / by a negative number

The number line has a solid circle at -1 and is shaded to the left.

300
Solve. Show all work.

⅕ x=3

What is

⅕x=3

5 ⅕ x=3*5

x=15

300
#3 Solve. Show all work.

6 - y/3 = 0

6-6 - y/3 = 0-6

- y/3 = -6

- y/3*-3 = -6*-3

y = 18

300
x < 9

Make sure to clearly mark where your circle is on the number line and which direction you are shading

The solution has an solid circle at 9 and is shaded to the left.
300
#30 The coach of the field hockey team can spend at most $475 on new team uniforms. The coach will order the uniforms online and pay a mailing cost of $6.50. If each uniform costs $29, how many uniforms can the coach order?

29u + 6.50 < 475

29u + 6.50 - 6.50 < 475-6.50

29/29u < 475/29

u < 16.4 SO the coach can order 16 uniforms

300

#13 Solve. Show all work. Graph the solution ⅔ - x/6 > -½

⅔ - x/6 > -&frac12

6*⅔ - 6*x/6 > 6*-½

4- x > -3

4- 4 - x > -3-4

-1/-1 x > -7/-1

x < 7 The sign switches direction because you are dividing by a negative

The number line has a shaded circle at 7 and is shaded to the left.

400
Solve. Show all work.

1.2x = 2.4

What is

1.2x = 2.4

1.2/1.2 x = 2.4/1.2

x = 2

400
#4 Solve. Show all work.

3 - 3.6x = 4.2

3*10 - 3.6*10x = 4.2*10

30 - 36x = 42

30-30 - 36x = 42-30

- 36x = 12

-36/-36x = 12/-36

x = -12/36=-12/12/36/12=-1/3

400
x < ⅓

Make sure to clearly mark where your circle is on the number line, which whole numbers it is in between and which direction you are shading

The solution has an open circle at ⅓ which is in between 0 and 1 and is shaded to the left.
400
#26 Laura want the average amount of money she spends each day on her four-day vacation to be no more than $64. On the first three days, she spends $71, $62, and $59. What is the greatest amount of money she can spend on the fourth day?

(71+62+59+x)/4 < 64 Add the 4 days of spending, including the fourth day which is x, the unknown.

4* (71+62+59+x)/4 < 4* 64

(71+62+59+x) < 256

192-192 +x < 256-192

x < 64 So she can spend up to $64 on day four

400

#15 Solve. Show all work. Graph the solution 9y-5 < 4y+15

9y-4y -5 < 4y-4y+15

5y -5+5 < 15+5

5y < 20

5/5y < 20/5

y < 4

The number line has a solid circle at 4 and is shaded to the left.

500
Solve. Show all work.

¾x = 6

What is

¾x = 6

4* ¾ x = 6*4

3x = 24

3/3x = 24/6

= 4

500
#5 Solve. Show all work. 7x - 5 = 3x + 4

7x-3x - 5 = 3x-3x + 4

4x - 5+5 = 4+5

4x = 9

4/4x = 9/4

x= 9/4

500

-3 < x

Make sure to clearly mark where your circle is on the number line and which direction you are shading

Switch the inequality to: x >-3 The solution has an open circle at -3 and is shaded to the right.
500
Kevin plans to sign up for p hours of training at a culinary school. The school offers two payment options as shown.

Option A: $8 per hour plus $200 for supplies Option B: $18 per hour, no fee for supplies

For how many hours of training is Option B less expensive than Option A?

18h<8h+200

18h - 8h < 8h - 8h + 200

10/10 < 200/10

h < 20 So option B is less expensive when you go for less than 20 hours

500

#18 Solve. Show all work. Graph the solution 3(x+1) > 5x+7

3x+3 > 5x+7 use the distributive property

3x-3x+3 > 5x-3x+7 balance variable term

3-7 > 2x+7-7 balance constant term

-4 > 2x

-4/2 > 2/2x

-2 > x OR x < -2 flip so the variable is on the left side

The number line has an open circle at -2 and is shaded to the left.

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