Solving Equations

Solve It

100

Solve and Verify: 

3/x = 5

x = 3/5

200

Solve and Verify:

x/4 + 1 = 5

x = 16

300

Solve and Verify:

4(a - 3) = 10

b = 22/4

400

Solve and Verify:

3b + 5 = 6b - 1

b = 2

500

Solve and Verify:

2(2x + 1) = 3(x -4)

x = -14

Model It

100

Solve the following equation using algebra tiles:

2x = 6 - x

x = 2

200

Use the Balance Scale Model and solve the equation:

4x = 3 - 2x

x = 1/2

300

Use the Balance Scale Model and solve the equation:

3(x -1) = 5

x = 8/3

400

Solve the following equation using algebra tiles:

-3(x - 2) = -6

x = 4

500

Use the Balance Scale Model and solve the equation:

2(x + 3) = -1(3x + 2)

x= -8/5

Fix It

100

Find the mistake in the following solution and fix it:

2(x + 1.5) = 6

2(x) + 2(1.5) = 6

2x + 3 = 6

2x + 3 - 3 = 6

2x = 6

2x/2 = 6/2

x = 3

Mistake: Forgot to subtract 3 from BOTH sides

Answer: x = 3/2

200

Find the mistake in the following solution and fix it:

3 - x/4 = 7

3 - x/4 -3 = 7 - 3

x/4 = 4

x = 16

Mistake: Forgot to keep (x/4) NEGATIVE

Answer: x = -16

300

Find the mistake in the following solution and fix it:

-2(x - 3) = 15

-2(x) - 2(-3) = 15

-2x - 6 = 15

-2x - 6 + 6 = 15 + 6

-2x = 21

-2x/-2 = 21/-2

x = -21/2

Mistake: Distributed (-2) wrong, it should've been :-2x + 6, NOT -2x -6

Answer: x = -9/2

400

Find the mistake in the following solution and fix it:

2(3x -6) = 3(5 -x)

6x - 12 = 15 - 3x

3x - 12 = 15

3x = 27

x = 9

Mistake: Subtracted 3x from both sides when we should've ADDED 3x to both sides.

Answer: x = 3

500

Find the mistake in the following solution and fix it:

(3x -1)/2 = x + 5 

2(3x -1)/2 = x + 5

3x - 1 = x + 5

3x - 1 + 1 = x + 5 + 1

3x = x + 6

3x - x = x + 6 - x

2x = 6

x = 3

Mistake: Forgot to multiple BOTH sides by 2

Answer: x = 11

Write It

100

Half a number plus 5 is 11.

Write an equation representing this situation and solve the problem.

Answer: 

 x/3 + 5 = 11

x = 12

200

Ahmed buys some shoes online for $23.00 per pair including tax, and the shipping is $5.00. If he decides to buy more pairs of those same shoes and it doesn't change the shipping cost, how many can he buy with $120.00?

Write an equation representing this situation and solve the problem.

Answer: Ahmed can buy 5 pairs of shoes.

 23x + 5 = 120

300

Maria bought notebooks for 3 dollars each and pens for 2 dollars each. She bought 5 more pens than notebooks. If she spent $40, how many notebooks and pens did Maria buy?

Write an equation representing this situation and solve the problem.

Answer: Maria bought 6 notebooks and 11 pens.

3x + 2(x+5) = 40

400

The sum of two numbers is 25. One of the numbers exceeds the other by 9. Find the numbers. 

Write an equation representing this situation and solve the problem.

Answer: The two numbers are: 8 and 17

x + (x + 9) = 25

x = 8

500

Peter has six times as many dimes as quarters in her piggy bank. He has $2.55 coins in his piggy bank. How many of each type of coin does she have?

Write an equation representing this situation and solve the problem.

Answer: Peter has 3 quarters and 18 dimes.

25x + 10(6x) = 255 

x = 3

Simplify It

100

Simplify the following equation so that it contains no decimals or fractions.

3x/4 - 5/8 = 2

Answer: 

2x = 7

==> x = 7/2

200

Simplify the following equation so that it contains no decimals or fractions.

x/3 - 1/4 = 5

Answer:

4x = 63

==> x = 63/4

300

Simplify the following equation so that it contains no decimals or fractions.

3 - 1.3x = 6.9

Answer:

x = -3

400

Simplify the following equation so that it contains no decimals or fractions.

7x/9 + 3 = x/3

4x = -27

500

Simplify the following equation so that it contains no decimals or fractions.

2.4 - 0.8x = 3.6x + 1.2

Answer:

4x = 1

==> x = 1/4