Solving Equations and Inequalities

Solving Equations and Inequalities

By Paul Roberts

Multiple Choice

Solve the equation: 4x + 3(x - 4) = 2(x + 4)

• x = 4

• x = 16/5

• x = 12/5

• x = 5

Multiple Choice

How many solutions does the equation have?

3(x + 2) = 3x + 5

• One Solution

• No Solution

• Infinitely Many Solutions

Multiple Choice

How many solutions does the equation have?

2x + 3 = 3 + 2x

• One Solution

• No Solution

• Infinitely Many Solutions

Multiple Choice

How many solutions does the equation have?

4(x + 3) = x + 6

• One Solution

• No Solution

• Infinitely Many Solutions

Multiple Choice

How many solutions does the equation have?

x + 45 = x + 47

• One Solution

• No Solution

• Infinitely Many Solution

Open Ended

Solve the equation: 6(x - 3) + 8 = 10 + 4x

Open Ended

Captain Sparrow solved the inequality below incorrectly. What was his mistake?

$$-2x\ +\ 4\ >\ 16$$  

$$-2x\ >\ 12$$  

$$x>-6$$  

Multiple Choice

Solve for x.

$$7x\ +\ 13\ =\ 76$$  

• x = 5

• x = 89/7

• x = 9

• x = 15

Multiple Choice

Solve for x.

$$4x\ +\ 12\ =\ 10x\ -\ 24$$  

• x = 4

• x = 6

• x = 8

• x = -5

Multiple Choice

Solve for x.

$$12x\ -5\ \ge\ 3x\ +\ 13$$  

• $$x\ \ge\ \frac{9}{8}$$  

• $$x\ \ge\ 3$$  

• $$x\ \ge\ \frac{8}{9}$$  

• $$x\ \ge\ 2$$  

Multiple Choice

Solve for x.

$$-8x\ +\ 10\ <-30$$  

• $$x\ >\ 5$$  

• $$x\ <\ 5$$  

• $$x\ >\ \frac{5}{2}$$  

• $$x<\frac{5}{2}$$  

Multiple Choice

Solve the compound inequality.

$$x-10=15\ \ or\ \ 3x+4<16$$  

• $$x=5\ or\ x\ <\ 4$$  

• $$x\ =\ 25\ or\ x<4$$  

• $$x=5\ and\ x<4$$  

• No Solution 

Multiple Choice

Solve the compound inequality.

$$8x+2=50\ \ and\ \ x+5=10$$  

• $$x=6\ and\ x=5$$  

• $$x=7\ and\ x=10$$  

• $$x=5\ and\ x=3$$  

• No Solution

Multiple Choice

In order to get a discount on game tickets at the county fair a person must be 5 years old or younger or older than 60. Which compound inequality models this scenario?

• $$x<5\ or\ x>60$$  

• $$x<5\ and\ x>60$$  

• $$x\le5\ and\ x>60$$  

• $$x\le5\ or\ x>60$$  

Multiple Choice

Select the property that proves that the equation has a solution set of all real numbers. If the solution set is not all real numbers, select Not All Real Numbers.

$$5\left(x+3\right)=5x+15$$  

• Commutative Property

• Associative Property

• Distributive Property

• Not All Real Numbers

Multiple Choice

Select the property that proves that the equation has a solution set of all real numbers. If the solution set is not all real numbers, select Not All Real Numbers.

$$10x\ +6=6+10x$$  

• Commutative Property

• Associative Property

• Distributive Property

• Not All Real Numbers

Multiple Choice

Select the property that proves that the equation has a solution set of all real numbers. If the solution set is not all real numbers, select Not All Real Numbers.

$$5x+3=8x+3$$  

• Commutative Property

• Associative Property

• Distributive Property

• Not All Real Numbers

Multiple Select

Select the property that proves that the equation has a solution set of all real numbers. If the solution set is not all real numbers, select Not All Real Numbers. Select more than one answer.

$$4\left(x+3\right)=12+4x$$  

• Commutative Property

• Associative Property

• Distributive Property

• Not All Real Numbers