Algebra I Nachala Analiza 10-11 Klass Ershova Goloborodko Reshenie C20a 1 Str Apr 2026

.The solution to the quadratic inequality is the interval between the roots: -1 Answer : А.П. Ершова, В.В. Голобородько

log2(2x−4)>log2(8)log base 2 of open paren 2 x minus 4 close paren is greater than log base 2 of 8 Since the base

log0.5(x+1)≥log0.5(4)log base 0.5 of open paren x plus 1 close paren is greater than or equal to log base 0.5 of 4 is between 0 and 1 ( We can remove the logs while keeping the

log0.5(x+1)≥-2log base 0.5 of open paren x plus 1 close paren is greater than or equal to negative 2 The argument must be positive:

Both arguments must be positive:

Rewrite the constant 3 as a logarithm with base 2:

log2(2x−4)>3log base 2 of open paren 2 x minus 4 close paren is greater than 3 the logarithmic function is increasing.

is greater than 1, the logarithmic function is increasing. We can remove the logs while keeping the inequality sign the same: 2x−4>82 x minus 4 is greater than 8 2x>122 x is greater than 12 x>6x is greater than 6 Both conditions must be met: . The intersection of these intervals is ✅ Answer : Problem 2: Solve the inequality