Question

What is the justification for each step solving the inequality? 2x+1<_3(x+1)/2 4x+2<_3(x+1) 4x+2<_3x+3 x+2<_3 x<_1 Multiplication or Division, property of order Distributive property Addition and subtraction property of order.

Answer 1

$2x+1\leq\dfrac{3(x+1)}{2}$

Multiplication property of equality (multiply both sides by 2)

$2(2x)+2(1)\leq\not2^1\cdot\dfrac{3(x+1)}{\not2_1}\\\\4x+2\leq3(x+1)$

Distributive property

$4x+2\leq(3)(x)+(3)(1)\\\\4x+2\leq3x+3$

Subtraction property of equality (subtract 3x from both sides)

$4x-3x+2\leq3x-3x+3\\\\x+2\leq3$

Subtraction property of equality (subtract 2 from both sides)

$x+2-2\leq3-2\\\\x\leq1$

Answer 2

2x+1 <= 3(x+1)/2

4x+2 <= 3(x+1) -------------->Multiplication or Division property of order

4x+2 <= 3x+3 -------------->Distributive property

  x+2 <= 3 ------------------>Addition and subtraction property of order.

     x<= 1 --------------------->Addition and subtraction property of order.