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 > ‚

Answer 1

Answer:

The solution of the given inequality is x > -9.

Step-by-step explanation:

The given inequality is

$4(x-3)+4<10+6x$

1. The distributive property:

$4x-12+4<10+6x$

2. Combine like terms:

$4x-8<10+6x$

3. The addition property of inequality: Add 8 on both the sides.

$4x-8+8<10+6x+8$

$4x<18+6x$

4. The subtraction property of inequality: Subtract 6x from both the sides.

$4x-6x<18+6x-6x$

$-2x<18$

5. The division property of inequality: Divide both sides by -2. The sign of inequality changes when we divide or multiply the inequality by  negative number.

$x>-9$

Therefore the solution of the given inequality is x > -9.

Answer 2

"Answer:

Let us walk through the steps involved in solving the given inequality:

Given: 4(x-3) + 4 < 10 + 6x

Step 1: The Distributive Property is Used

4x - 12 + 4 < 10 + 6x

Step 2: Now we combine the like terms  on each side of the inequality

4x - 8< 10 + 6x

Step 3: The Addition Property : Adding 8 on both sides

4x-8+8<10+6x+8

4x<6x+18

Step 4: The Subtraction Property: Subract 6x from both sides of the inequality

4x-6x<6x+18-6x

-2x<1

Step 5: The division Property : Divide both sides of the inequality by 2.

The rule behind the division / multiplication property of inequality is that when we divide or multiply the inequality by a negative number, the inequality sign changes.

-2x<18=>x>-9

The solution for the given inequality is x>-9."