Question

Identify the line that contains the error in this solution and correct the work for that line.

Answer 1

Line 1: -2(x + 1) - 3 ≥ 11
Line 2: -2x + -2 - 3 ≥ 11
Line 3: -2x + -5 ≥ 11
Line 4: -2x ≤ 16
Line 5: x ≤ -8

Answer 2

Do you know the first step?

Answer 3

Simplify like terms?

Answer 4

Well lets start with line one,

You want to solve it just like an equation.

Step 1 would be to distribute.

Answer 5

-2(x + 1) - 3 ≥ 11

-2x - 1 - 3 ≥ 11

Answer 6

okay.
-2x - 1 - 3
1 - 3 = - -1

Answer 7

If the answer is -1, then we went wrong on line two.

Answer 8

-2(x + 1) - 3 ≥ 11
-2x - 1 - 3 ≥ 11
-2x - 4 ≥ 11
-2x ≥ 11 + 4
-2x ≥ 15
-2x 15
--- ≥ ----
-2 -2

Answer 9

Line 4: -2x ≤ 16
Line 5: x ≤ -8

We see here that -2 is on the left, upon dividing by a negative the signs switch, also. We went wrong on line 5.

Answer 10

so we should add three to both sides at line 2?

Answer 11

Line 1: -2(x + 1) - 3 ≥ 11 (Original equation.)

Line 2: -2x + -2 - 3 ≥ 11 (Distributed)

Line 3: -2x + -5 ≥ 11 (Added like terms.)

Line 4: -2x ≤ 16 (Added +5 to 11.)

Line 5: x ≤ -8 (Divided by -2, but the signs didn't switch. Line: 5 is wrong.)

The equation should say:

\[x \ge -8\]

Answer 12

Remember, that upon dividing by a negative number the sign switches.

Answer 13

okay, I understand now.
Thank you so much. :)

Answer 14

I always return the favor of a medal.