23-24 Alg 2. Semester Review

Solve the following equation. Be sure to check for extraneous solutions.

• {-10,10}

• 10

• -10

• No Solution

Answer explanation

Step 1: Isolate absolute value. Which means need to add 4 to both sides.

Step 2: Split into 2 equations.

Step 3: Solve each equation

Step 4: Check for extraneous solutions. When you plug each answer into the original problem you see they both work.

Solve the following equation. Be sure to check for extraneous solutions.

• {-4,3}

• -4

• 3

• No Solution

Answer explanation

Step 1: Need to isolate the absolute value. Can NEVER distribute into absolute values which means you have to divide both sides by -3

Step 2: You see the absolute value equals a negative number which is not possible. Meaning you can stop here and say NO Solution.

You can also continue with the steps and when you plug in x= -4 and x= 3 you get them both to be extraneous.

Solve the following equation. Be sure to check for extraneous solutions.

• 2

• {-2,2}

• 14

• No Solution

Answer explanation

Step 1: Isolate absolute value by dividing both sides by 2

Step 2: Split into 2 equations. Remember to keep the terms inside the absolute value the same.

Step 3: Solve both equations

Step 4: Check for extraneous solutions.

Solve the following inequality and select the correct representation in interval notation.

• 
• 
• 
• No Solution

Answer explanation

Step 1: Isolate absolute value. Need to add 4 first THEN divide both sides by 2.

Step 2: Split into 2 inequalities. Remember to switch the inequality and sign of the second inequality.

Step 3: Solve each one separately.

Step 4: Graph on number line to determine interval notation.

Solve the following inequality and select the correct representation in interval notation.

• 
• 
• 
• No Solution

Answer explanation

Step 1: Isolate absolute value. Need to divide by 3 (you can NEVER distribute into absolute values)

Step 2: Split into 2 inequalities. Remember to switch the inequality AND sign of the second inequality.

Step 3: Solve each one separately.

Step 4: Graph on number line to determine interval notation.

Solve the following inequality and select the correct representation in interval notation.

• 
• 
• 
• No Solution

Answer explanation

Step 1: Isolate absolute value. Need to add 6 first THEN divide both sides by -3. When you divide (or multiply) both sides by a negative FLIP the inequality. Meaning after step 1 you get a LESS THAN symbol.

Step 2: Split into 2 inequalities. Remember to switch the inequality and sign of the second inequality.

Step 3: Solve each one separately.

Step 4: Graph on number line to determine interval notation.

Solve the following inequality and select the correct representation in interval notation.

• 
• 
• 
• No Solution

Answer explanation

An absolute value can never be negative or less than a negative number.

Solve the equation:

• 16

• -8

• 7

• -2

Answer explanation

Step 1: Multiply both sides by 4. Make sure you multiple BOTH terms on the right side by 4

Step 2: Move y's to one side and anything without a y on the other side

Step 3: Divide to get y by itself

Solve the equation:

• 3

• -9

• -1

• 1

Answer explanation

Step 1: Subtract w and subtract 2 to the right side of the equation

Step 2: Multiple both sides by 5. Remember to multiply BOTH terms on the right by 5.

Step 3: Move w's to one side and anything without a w to the other side of the equal sign.

Step 4: Get w by itself

Solve the equation:

• 5

• -5

• 2

• 4

Answer explanation

Step 1: Get everything outside parenthesis to the other side> First add 3 then divide both sides by 4.

Step 2: Parentheses can go away. Then subtract 2 on both sides

Step 3: Get rid of fraction by multiplying both sides by 4. This leaves the left side with 3w+5 and on the right side you DISTRIBUTE the 4 so you get =5w+4

Step 4: Move anything with a w to one side of the = sign and anything that doesn't have a w to the other side. Then solve for w.