Review Solving linear equations and inequalities

Review Solving linear equations and inequalities

This assignment will give you bonus points to be used either for a missing assignment or added to your test score.

Solving equations

• The purpose of solving an equation whether it is one, two or multi-step is to isolate the variable.

• Combining like terms and using the distributive property to simplify the sentence before solving will help when looking at the terms.

• Review your notes and add any things you feel will help you on your test to the note card. Know what like term means and how to work with the integers. The following will help get you ready for this part of the test.

Multiple Choice

Solve for x. 
2x + 1 = 3x + 1 - x

• x = 0
• x = 1
• No Solution
• Infinite Solutions

Multiple Choice

Find the error in the problem below
19 - 2k = 3k - 1
     +3k   +3k
19 + 1k = -1
-19           -19
k = -20

• They should have divided by 1 for the last step
• They should add 19 instead of subtracting 19
• I can not find an error
• Instead of adding 3k they should subtract 3k

Multiple Choice

Solve:
2(2x + 3) = -6(x + 9)

• 1.2
• 6
• -6
• 7.5

Multiple Choice

Solve:
 $3x+15=3\left(x+5\right)$  

• No Solution

• x = 15

• All Real Numbers

• x = 0

Multiple Choice

What property is this?

9(b + 0.5) = 9b + 4.5

• Inverse

• Associative

• Distributive

• Communitive

Multiple Choice

Solve:  6z + 3 -4z = 9

• z = 3
• z = 60
• z = 30
• z = 1

Multiple Choice

What is the first step in solving the following problem?

2x+10=22

• Add 10 to each side

• Divide by 2

• Subtract 10 from each side

• Multiply by 10

Multiple Choice

Solve:
2(4x - 3) - 8 = 4 + 2x

• x = 5/3
• x = 3
• x = 1
• x = 2

Multiple Choice

Solve the equation
-8x - 8 + 3(x - 2) = -3x + 2

• x = -8
• x = 8
• x = 2
• x = -2

Multiple Choice

Solve the equation:

3(x - 1) = 2x + 9

• x = 12

• no solution

• x = 10

• x = 6

Multiple Choice

Solve:
7x - 3x - 8 = 24

• 8
• -8
• 3.2
• 4

Story Problems

• We looked at 5 types of different story problems.

• The hardest part is in the translation. We did a story problem activity in class (e-learning day) that will help you review for the test.

• The ones given here will help you practice.

Multiple Choice

Write an equation to represent this word problem.

• 40 - 2f = 8
• 40 + 2f = 8
• 8 - 2f = 40
• 40 = 2f - 8

Multiple Choice

Jim paid a gym membership fee of $50, plus $20 per month.  Jim has paid a total of $290 to the gym.  Which equation matches this situation?

• 50 + 20m = 290
• 20 + 50m = 290
• 50 + 20 = m
• 50m - 20 = 290

Multiple Choice

331 students went on a field trip. Six buses were filled and 7 students traveled in cars. How many students were in each bus? Write an equation that matches this situation.

• 331=7x+6
• 331=13x
• 331=6x+7
• 331-7=6x

Multiple Choice

What equation matches this situation?
Robyn had some video games then bought 4 more.  Now she has a total of 10 games.

• v - 4 = 10
• v + 4 = 10
• 10 - 4 = v
• Answer not Given

Multiple Choice

It took a sled dog team 8.5 hours to travel 161.5 kilometers. What was the average speed of the sled dog team in kilometers per hour?

• 19
• 20
• 21
• 153

Literal Equations and formulas

• When solving a literal equation, you are given 2 or more variables and asked to isolate a specific variable. Use the skills you know from solving equations to isolate the variable asked for.

• Formulas are where you substitute the values in for the variables and solve for the missing variable.

• Both of these will be on the test. Make sure you understand the variable substitution for the formula section. You may want to put a few formulas down example how do you find area?

Multiple Choice

Solve for r.

• A
• B
• C
• D

Multiple Choice

Solve for r.

• A
• B
• C
• D

Multiple Choice

If 3x + y = 7
and z/(2x) = 9,
what is the
product of y and z?

• 7 - 3x
• 18x
• 7 + 15x
• 126x - 54x²

Multiple Choice

Solve the literal equation for the given variable.

• 2A/h
• 2/(h)
• 2Ah
• Ah/2

Multiple Choice

Solve for a.

• a = pw
• a = p/w
• a = w/p
• a = w + p

Multiple Choice

pV = nRT
solve for R

• R= pV/nT
• R= p/n + V/T
• R= pV - nT
• R= (pV-n)/T

Multiple Choice

The variable, k, is being divided by 11. How should you isolate the variable?

 $16=\frac{k}{11}$  

• Divide both sides by 11

• Multiply both sides by 11.

• Add 11 to both sides.

• Subtract 11 to both sides.

Solving Inequalities

• The only difference between solving and equation and an inequality is the sign.

• Remember the rule when working with negatives in multiplication and division of an inequality.

• You will need to be able to draw inequalities on a line. The information given in the notes should be added to your card for the test.

Multiple Choice

Solve the following compound inequality:

−8 < 2(x + 4) or −3x + 4 > x − 4

• No solutions

• x < −8 or x < 2

• x > −8 or x < 2

• x < −8 and x < 2

Multiple Choice

Solve the following compound inequality:

3x − 4 < −13 or 7x + 1 > 22

• All Real numbers

• x > 3 and x > −9

• The answer is not listed

• x < −3 or x > 3

Multiple Choice

What inequality is graphed?

• x > 2 and x ≤ −3

• x > 2 and x < −3

• x > 2 or x ≤ −3

• x > 2 or x < −3

Multiple Choice

Solve the following compound inequality:

−4x + 1 ≤ 21 and 5x + 2 < 22

• x > −5 or x ≤ 4

• x ≥ −5 or x < 4

• x > −5 and x ≤ 4

• x ≥ −5 and x < 4

Multiple Choice

You flip an inequality symbol when you...

• subtract
• multiply and divide only
• multiple by a negative number
• multiple or divide by a negative number

Multiple Choice

Which of the following is the solution to the  inequality below
-5x -10 < 20

• x > -6
• x < -6
• x > -2
• x <  -2

Multiple Choice

What is the inverse operation of division?

• Division

• Multiplication

• Addition

• Subtraction

Multiple Choice

What is the next step when solving for B?

• 5B ≤ 17.5

• 5B ≤ 12.5

Multiple Choice

What is the common denominator of 7/2 and 2/3?

• 5

• 6

• 14

• 21

Multiple Choice

Which figure shows the inequality x > -4?

• Figure 1
• Figure 2
• Figure 3
• Figure 4

Multiple Choice

Pick the correct inequality.

• A
• B
• C
• D

Multiple Choice

Solve: 3(x - 2) < 2(x + 9)

• x < 24

• x > -24

• x < 12

• x > 18

Multiple Choice

Which inequality symbol has a graph with an open (empty) circle?

• <

• ≤

Multiple Choice

Solve and choose the correct graph:

• A
• B
• C
• D

Multiple Choice

Solve:
7(x + 3) < 5x + 13

• x>-4
• x < 17
• x<-4
• x > -17

Multiple Choice

Solve:
3(x - 2) < 2(x + 9)

• x<24
• x>12
• x<12
• x>24

Multiple Choice

Do you flip the sign?
-3x + 2  ≤  22

• YES
• NO

Multiple Choice

When graphing an inequality, what does a closed circle mean?

• The number is not included in the list of answers.
• The number is included in the list of answers.

Multiple Choice

What inequality does the number line graph represent?

• x > 5
• x < −5
• x ≥ 5
• x ≥ −5

That's All Folks!

See you with your card ready for the test. The Review for chapter 2 which is in the textbook needs to be written out on notebook paper, problems included.