Question

A) 2|x-4|=6b) 12|2x-5|=-60​

Answer 1

a) 2|x-4|=6

• Делим оби части уравнения на 2

|x-4|=3

• Используя определение модуля, представьте уравнение с модулем в виде двух отдельных уравнений

$\left \{ {{x-4=3} \atop {x-4=-3}} \right.$

• Решить уравнения относительно x

$\left \{ {{x=3+4} \atop {x=-3+4}} \right.$

$\left \{ {{x=7} \atop {x=1}} \right.$

Ответ: $\left \{ {{x_{1} =1} \atop {x_{2} =7}} \right.$

b) 12|2x-5|=-60​

• Поскольку левая часть всегда положительная или 0, а правая часть всегда отрицательная, утверждение ложно для любого значения x

Ответ: x ∈ ∅

Answer 2

Let's solve each of these absolute value equations step by step:

A) 2|x - 4| = 6

1. Start by isolating the absolute value expression on one side of the equation: |x - 4| = 3

2. Now, you have two cases to consider because the absolute value of a number can be either positive or negative:

   Case 1: x - 4 = 3 Solve for x: x = 3 + 4 x = 7

   Case 2: x - 4 = -3 Solve for x: x = -3 + 4 x = 1

So, the solutions for equation A are x = 7 and x = 1.

B) 12|2x - 5| = -60

1. Start by isolating the absolute value expression on one side of the equation: |2x - 5| = -60 / 12 |2x - 5| = -5

2. Absolute values are always non-negative, so an absolute value can never equal a negative number. Therefore, this equation has no solutions.

So, equation B has no real solutions.