Question

|х|=51|х|=17|х|=-117|х|-2|х|-11=-10|х|+19​

Answer 1

х¹=-51 ; х²=51

х¹=-17; х²=17

х¹=-11 х²=11

Answer 2

Let's solve the equation step by step.

|х| = 51 |х| = 17 |х| = -117

These three equations involve the absolute value of х. In each case, the absolute value of х is equal to a specific number, but the absolute value of a real number is always non-negative. Therefore, there are no real solutions for these equations because you cannot have an absolute value equal to a negative number.

However, if you want to solve the equation involving absolute values:

|х - 2| - 11 = -10 |х| + 19

We can first isolate the absolute value on the right side of the equation:

|х - 2| = -10 |х| + 19

Now, let's consider two cases:

Case 1: х is positive or zero (х ≥ 0) In this case, |х| = х, so the equation becomes:

|х - 2| = -10х + 19

Now, let's split it into two equations:

1. х - 2 = -10х + 19 (because |a| = a when a is non-negative)
2. х - 2 = 10х - 19 (because |a| = -a when a is non-negative)

Solve each equation:

1. х - 10х = 19 + 2 -9х = 21 х = -21/9 х = -7/3

2. х - 10х = -19 + 2 -9х = -17 х = -17/(-9) х = 17/9

So, when х is positive or zero, there are two solutions: х = -7/3 and х = 17/9.

Case 2: х is negative (х < 0) In this case, |х| = -х, so the equation becomes:

|х - 2| = -10(-х) + 19

Now, let's split it into two equations:

1. х - 2 = 10х + 19 (because |a| = -a when a is negative)
2. х - 2 = -10х + 19 (because |a| = a when a is negative)

Solve each equation:

1. х - 10х = 19 + 2 -9х = 21 х = -21/9 х = -7/3

2. х + 10х = 19 + 2 11х = 21 х = 21/11

So, when х is negative, there are two solutions: х = -7/3 and х = 21/11.

In summary, the equation has four solutions: х = -7/3, х = 17/9, х = -7/3, and х = 21/11.