Question

1) |y-3| = 7. 2) ||2-t|+5|=10.

Answer 1

1)|у-3|=7
[у-3=7;у=10
[у-3=-7;у=-4

2)||2-t|+5|=10

a)|2-t|+5=10
|2-t|=5
2-t=5;t=-3
2-t=-5;t=7

b)|2-t|+5=-10
|2-t|=-15
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ответ -3;7

Answer 2

1)
$|y - 3| = 7 \\ \\ y - 3 = 7 \\ y - 3 = - 7 \\ \\ y = 7 + 3 \\ y = - 7 + 3 \\ \\ y = 10 \\ y = - 4$
Ответ: -4; 10.

2)
$| |2 - t| + 5| = 10 \\ \\ |2 -t | + 5 = 10 \\ |2 - t| + 5 = - 10 \\ \\ |2 - t| = 5 \\ |2 - t| = - 15$
второе уравнение не имеет корней, так как модуль не может равняться отрицательному числу.

$|2 - t| = 5 \\ \\ 2 - t = 5 \\ 2 - t = - 5 \\ \\ - t = 3 \\ - t = - 7 \\ \\ t = - 3 \\ t = 7$
Ответ: -3; 7.

Answer 3

To solve the given equations, we need to find the values of the variables that satisfy the equations. Let's solve each equation step by step:

1. |y - 3| = 7

To remove the absolute value, we have two cases to consider:

Case 1: y - 3 = 7 Add 3 to both sides: y = 7 + 3 y = 10

Case 2: y - 3 = -7 Add 3 to both sides: y = -7 + 3 y = -4

So, the two solutions for the equation are y = 10 and y = -4.

2. ||2 - t| + 5| = 10

To remove the double absolute value, we again have two cases:

Case 1: |2 - t| + 5 = 10 Subtract 5 from both sides: |2 - t| = 10 - 5 |2 - t| = 5

Now, we have two sub-cases to consider within this case:

Sub-case 1.1: 2 - t = 5 Subtract 2 from both sides: -t = 5 - 2 -t = 3

Multiply by -1 to solve for t: t = -3

Sub-case 1.2: 2 - t = -5 Subtract 2 from both sides: -t = -5 - 2 -t = -7

Multiply by -1 to solve for t: t = 7

Case 2: |2 - t| + 5 = -10

Since an absolute value can't be negative, there are no solutions within this sub-case.

So, the two solutions for the equation are t = -3 and t = 7.