Question

Select the graph of the solution set that would represent the following expression. 2 ( x + 1 ) > 3 x − 2

Answer 1

We are given with an inequality and need to find it's solution set and need to represent it on number line too. Let's start !!!!

`{:\implies \quad \sf 2(x+1)\> 3x-2}`

`{:\implies \quad \sf 2x+2\> 3x-2}`

Subtracting 2x from both sides ;

`{:\implies \quad \sf \cancel{2x}+2-\cancel{2x}\> 3x-2-2x}`

`{:\implies \quad \sf 2\> x-2}`

Adding 2 to both sides :

`{:\implies \quad \sf 2+2\> x-\cancel{2}+\cancel{2}}`

`{:\implies \quad \sf 4\> x }`

`{:\implies \quad \sf x\< 4}`

`{:\implies \quad \bf \therefore \quad \underline{\underline{x\in (-\infty,4)}}}`

Refer to the attachment for representation

Answer 2

Hey there!

2(x + 1) > 3x - 2

DISTRIBUTE 2 WITHIN the PARENTHESES:

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

CONVERSION:

2x + 2 > 3x - 2

SUBTRACT 2 to BOTH SIDES:

-x + 2 - 2 > -2 - 2

SIMPLIFY IT!

NEW EQUATION:

-x > -4

CONVERSION 2:

-1x > -4

DIVIDE -1 to BOTH SIDES

-1x/-1 > -4/-1

SIMPLIFY IT!

x < 4

Therefore, your answer is: x < 4

Good luck on your assignment & enjoy your day!

~Amphitrite1040:)