Solving Equations and Word Problems

Equations

100

What is the first step to solve the equation 2x+3=11?

To solve 2x+3=11, the first step is to subtract 3 from both sides: 2x=8.

200

Solve the equation 3(x−4)=9.

Solve 3(x−4)=9:

1. Distribute: 3x−12=9
2. Add 12 to both sides: 3x=21
3. Divide by 3: x=7

300

If 5x+2=22, what is the value of x?

If 5x+2=22:

1. Subtract 2 from both sides: 5x=20
2. Divide by 5: x=4

400

Solve 4(x+1)−5=15 and show your work.

To solve 4(x+1)−5=15:

1. Distribute: 4x+4−5=15
2. Combine like terms: 4x−1=15
3. Add 1 to both sides: 4x=16
4. Divide by 4: x=4

500

What is the solution to 7x−3=4x+9?

To solve 7x−3=4x+9:

1. Subtract 4x from both sides: 3x−3=9
2. Add 3 to both sides: 3x=12
3. Divide by 3: x=4

Word Problems

100

A garden has a perimeter of 30 meters. If the length is 7 meters, what is the width?

The width of the garden is 30−2×7=16 meters.

200

The total cost of 3 notebooks and 2 pencils is $8. If each notebook costs $2, how much does each pencil cost?

If the total cost is $8 and each notebook is $2, then:

• Total cost of notebooks: 3×2=6
• Cost of pencils: 8−6=2
• Each pencil costs 2/2=1 dollar.

300

A rectangle's area is 48 cm². If its length is 8 cm, what is its width?

The width of the rectangle is 48/8=6 cm.

400

A bike costs $120. If you save $15 per week, how many weeks will it take to save enough to buy the bike?

To save $120 at $15 per week, it will take 120/15=8 weeks.

500

If a book costs $15 and you have $60, how many books can you buy?

If a book costs $15 and you have $60, you can buy 60/15=4 books.

Comparing Solutions

100

How would you solve x+5=12 using arithmetic?

To solve x+5=12 using arithmetic, subtract 5 from both sides: x=7.

200

Compare the algebraic solution to 4x=20 with the arithmetic method. What are the steps?

For 4x=20:

• Algebraic: Divide both sides by 4 to get x=5.
• Arithmetic: Recognize that 20 divided by 4 equals 5.

300

For the equation 2(x+3)=14, explain the sequence of operations for both solutions.

For 2(x+3)=14:

• Algebraic: Divide by 2: x+3=7, then subtract 3: x=4.
• Arithmetic: Recognize that 14 divided by 2 is 7, then subtract 3.

400

If 3x−4=8, how would you solve it algebraically and arithmetically?

For 3x−4=8:

• Algebraic: Add 4 to both sides: 3x=12, then divide by 3: x=4.
• Arithmetic: Recognize that 8 plus 4 is 12, then divide by 3.

500

Explain the differences in process when solving 5(x−2)=15 using algebra vs. arithmetic.

For 5(x−2)=15:

• Algebra: Divide by 5: x−2=3, then add 2: x=5.
• Arithmetic: Recognize that 15 divided by 5 is 3, then add 2.

Operations

100

What operation would you perform first to isolate x in x−3=7?

To isolate x in x−3=7, you would add 3 to both sides: x=10.

200

If you have the equation 2x+6=14, what operation do you perform next after subtracting 6?

In the equation 2x+6=14, after subtracting 6 from both sides, you would then divide by 2: 2x=8 followed by x=4.

300

Identify the sequence of operations used to solve x/4+2=5.

To solve x/4+2=5:

1. Subtract 2 from both sides: x/4=3
2. Multiply both sides by 4: x=12.

400

What operation do you use last in the equation 3x=18 to find x?

In the equation 3x=18, you would divide by 3 last to find x: x=6

500

Describe the order of operations needed to solve 5+2x=15.

To solve 5+2x=15, you would first subtract 5 from both sides: 2x=10, then divide by 2: x=5.