equation and Inequality

Solving Equations

To solve an equation, you may

• Add a number to both sides.

• Subtract a number from both sides.

• Multiply both sides by a number.

• Divide both sides by a number.

Solve: x + 1 = 5

x + 1 – 1 = 5 – 1

x = 4

Solve: x – 2 = 6

x – 2 + 2 = 6 + 2

x = 8

Solve: 3x = 9

3x/3 = 9/3

x = 3

Solve: x/5 = 8

5(x/5) = 5(8)

x = 40

Solve: 2x – 1 = 6

2x – 1 + 1 = 6 + 1

2x = 7

2x/2 = 7/2

x = 3.5

Inequalities

2x + 1 > 5 is an inequality.

To solve an inequality, you may

• Add a number to both sides.

• Subtract a number from both sides.

• Multiply both sides by a number.

• Divide both sides by a number.

Note that if you multiply/divide an inequality by a negative number, the inequality sign will reverse.

– x < – 3

x > 3

Solving Linear Inequalities

Solve: 2x + 1 > 5

2x + 1 – 1 > 5 – 1

2x > 4

2x / 2 > 4 / 2

x > 2

Solve: 5x + 10 > 2x + 22

5x + 10 – 10 > 2x + 22 – 10

5x > 2x + 12

5x – 2x > 2x + 12 – 2x

3x > 12

x > 4

Solve: 1 – 2x > 5

1 – 2x – 1 > 5 – 1

– 2x > 4

(–1) (–2x) < (–1) (4)

Since we multiply both sides by – 1, the inequality sign is reversed.

2x < – 4

2x / 2 < – 4 / 2

x < – 2

1. Find the smallest and largest integer x such that – 3 < 2x – 5 < 10

2. Jimmy has $20 and wants to rent a bicycle. The rental shop charges $1.50 per hour and a fixed charge of $2.00. Find the maximum number of hours he can rent the bicycle from the shop.

3. Raihan is paid a fixed salary $50 per day and $15 commission for every laptop he sells. Find the minimum number of laptops that he must sell, to earn at least $150 for the day.