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Core Connections: Course 2

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Core Connections: Course 2 View details

1. Section 6.1

Finish the assignment

Continue to next subchapter

Exercise 43 Page 336

Practice makes perfect

We can determine whether 2 is a solution by substituting it into the inequality and simplifying using the order of operations.

3x-2<2-2x

x= 2

3( 2)-2? <2-2( 2)

Multiply

6-2? <2-4

Subtract term

4 < - 2 *

Since 4 is not less than - 2, we can see that 2 is not a solution.

We can determine whether 12 is a solution by substituting it into the inequality and simplifying using the order of operations.

3x-2<2-2x

x= 1/2

3( 1/2)-2? <2-2( 1/2)

MoveRightFacToNumOne

1/b* a = a/b

3/2-2? <2-2/2

Calculate quotient

1.5-2? <2-1

Subtract term

- 0.5 < 1 ✓

Since - 0.5 is less than 1, we can see that 12 is a solution.

We can determine whether - 3 is a solution by substituting it into the inequality and simplifying using the order of operations.

3x-2<2-2x

x= - 3

3( - 3)-2? <2-2( - 3)

a(- b)=- a * b

- 3(3)-2? <2-2(- 3)

MultNegNegOnePar

- a(- b)=a* b

- 3(3)-2? <2+2(3)

Multiply

- 9-2? <2+6

Subtract term

- 11 < 8 ✓

Since - 11 is less than 8, we can see that - 3 is a solution.

We can determine whether 23 is a solution by substituting it into the inequality and simplifying using the order of operations.

3x-2<2-2x

x= 2/3

3( 2/3)-2? <2-2( 2/3)

▼

Simplify

MoveRightFacToNum

a/c* b = a* b/c

3(2)/3-2? <2-2(2)/3

Multiply

6/3-2? <2-4/3

Calculate quotient

2-2? <2-4/3

a = 3* a/3

2-2? <2(3)/3-4/3

Multiply

2-2? <6/3-4/3

Subtract fractions

2-2? <6-4/3

Subtract term

0 < 2/3 ✓

Since 0 is less than 23, we can see that 23 is a solution.

Subchapter links

6.1.1 Comparing Expressions p.322-323

6.1.2 Comparing Quantities with Variables p.327-328

6.1.3 One Variable Inequalities p.331-332

6.1.4 Solving One Variable Inequalities p.336-337