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Which of the following is the solution to the inequality below?

-3/2(x-1/3)> -5x

A. x> -3/35
B. x>2/21
C. x< 2/21
D. x< -3/35

User Dwhitz
by
5.1k points

1 Answer

6 votes

Answer:1/3

Explanation:

Rearrange the equation by subtracting what is to the right of the greater than sign from both sides of the inequality :

3/2*(x-1/3)-(-5*x)>0

Step by step solution :

STEP

1

:

1

Simplify —

3

Equation at the end of step

1

:

3 1

(— • (x - —)) - -5x > 0

2 3

STEP

2

:

Rewriting the whole as an Equivalent Fraction

2.1 Subtracting a fraction from a whole

Rewrite the whole as a fraction using 3 as the denominator :

x x • 3

x = — = —————

1 3

Equivalent fraction : The fraction thus generated looks different but has the same value as the whole

Common denominator : The equivalent fraction and the other fraction involved in the calculation share the same denominator

Adding fractions that have a common denominator :

2.2 Adding up the two equivalent fractions

Add the two equivalent fractions which now have a common denominator

Combine the numerators together, put the sum or difference over the common denominator then reduce to lowest terms if possible:

x • 3 - (1) 3x - 1

——————————— = ——————

3 3

Equation at the end of step

2

:

3 (3x - 1)

(— • ————————) - -5x > 0

2 3

STEP

3

:

3

Simplify —

2

Equation at the end of step

3

:

3 (3x - 1)

(— • ————————) - -5x > 0

2 3

STEP

4

:

Equation at the end of step

4

:

(3x - 1)

———————— - -5x > 0

2

STEP

5

:

Rewriting the whole as an Equivalent Fraction :

5.1 Subtracting a whole from a fraction

Rewrite the whole as a fraction using 2 as the denominator :

-5x -5x • 2

-5x = ——— = ———————

1 2

Adding fractions that have a common denominator :

5.2 Adding up the two equivalent fractions

(3x-1) - (-5x • 2) 13x - 1

—————————————————— = ———————

2 2

The equation at the end of step

5

:

13x - 1

——————— > 0

2

STEP

6

:

6.1 Multiply both sides by 2

6.2 Divide both sides by 13

x-(1/13) > 0

Solve Basic Inequality :

6.3 Add 1/13 to both sides

x > 1/13

User Chris Voth
by
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