Question

What is the missing step in solving the inequality 4(x – 3) + 4 < 10 + 6x? 1. The distributive property: 4x – 12 + 4 < 10 + 6x 2. Combine like terms: 4x – 8 < 10 + 6x 3. The addition property of inequality: 4x < 18 + 6x 4. The subtraction property of inequality: –2x < 18 5. The division property of inequality: ________

Answer 1

the missing step is multiplication on the side with no x.

Answer 2

Division property of inequality: x > - 9

Explanation:

Given, the inequality 4(x-3)+ 4 < 10+6x

Distributive property: a. (b+c)=a.b+a.c

The distributive property : 4x-12+4 < 10+ 6x

The combin like terms : 4x-8 <10+6x

Adding property: when we add two integers then we get a new value of an integer.

The addition property of inequality: 4x <18+6x

Subtraction property: when we subtract an ineteger number from other ineteger number then we get a new integer value.

4x-6x < 18

By subtraction property : -2x < 18

Division Property : when a dividened divided by divisor we get the value of quotient .

-2x < 18

-x <
`(18)/(2)`

-x < 9

after multiplying by -1 we get

x > -9

Because when we multiply by negative sign on both side of inequality then the sign of inequality changes.

Hence, The division property of inequality: x > -9.