Math Problem Statement

Solve the following algebra equations: 1. -8/x = -2/(x+1) 2. (18/4)x = 81/(2x) 3. 5(x + 7) - 3(x - 2) = 0 4. (x - 6) = sqrt(25/9) 5. -2(x - 4) - 5.1 = 9(x + 3.5)

Solution

Let's go through the solutions for each of these algebra problems step-by-step.

1. Solve: 8x=2x+1-\frac{8}{x} = -\frac{2}{x+1}

First, cross-multiply to eliminate the fractions:

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Math Problem Analysis

Mathematical Concepts

Algebra
Equations
Linear equations
Rational equations
Square roots

Formulas

Cross-multiplication
Distributive property
Square root

Theorems

Equality of fractions
Basic algebraic operations

Suitable Grade Level

Grades 9-11