Claire’s mother is 4 years more than twice Claire’s age. The sum of their ages is 58 years.

Let x = Claire's age
Claire’s mother is 4 years more than twice Claire’s age = 2x + 4
The sum of their ages is 58 years:
x + 2x + 4 = 58
3x + 4 = 58
3x = 54
x = 18

Claire's age = 18
Claire’s mother = 2(18)+4 = 36 + 4 = 40

claire's age = x

claire's mothers age = 2x+4 ( 4 more than twice claire's age)

sum is addition

x + 2x+4 = 58

add like terms ( x +2x = 3x)

3x +4 = 58

subtract 4 from each side:

3x = 54

divide both sides by 3
x = 54 /3
x = 18

Claire is 18 years old
 Claire's mother is  2*18 = 36 +4 = 40 years old