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: ________

x < –9
x > –9
x < x is less than or equal to negative StartFraction 1 Over 9 EndFraction.
x > –x is greater than or equal to negative StartFraction 1 Over 9 EndFraction.

Answer 1

✦ Given that

• 4(x - 3) + 4 < 10 + 6x

✦ We need to find

• The value of x

`\longleftrightarrow\rm{4x-12+4 < 10+6x}`

`\longleftrightarrow\rm{4x-8 < 10+6x}`

`\longleftrightarrow\rm{4x-6x < 10+8}`

`\longleftrightarrow\rm{-2x < 18}`

`\longleftrightarrow\rm{x > -9}`

Therefore x > -9

Answer 2

The missing step is to subtract 4x from both sides of the inequality:

4x - 8 < 10 + 6x

-2x - 8 < 10

Then, add 8 to both sides of the inequality:

-2x < 18

Finally, divide both sides by -2 and remember to flip the inequality sign since we are dividing by a negative number:

x > -9

Therefore, the answer is x > –9