21 Solve each of the following equations.
(a) $4 (x + 1) - 5 (x + 6) = 3 x + 4$
(b) $\frac{4 x + 1}{3} - \frac{x - 2}{4} = 2$

Answer

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Answer

(b) Solve for x: $x = \frac{14}{13}$

Steps

Step 1 ：(a) Distribute and combine like terms: $4 (x + 1) - 5 (x + 6) = 3 x + 4$ becomes $- x - 26 = 3 x + 4$

Step 2 ：(a) Solve for x: $x = - \frac{15}{2}$

Step 3 ：(b) Find common denominator and combine fractions: $\frac{4 x + 1}{3} - \frac{x - 2}{4} = 2$ becomes $\frac{13 x}{12} + \frac{5}{6} = 2$

Step 4 ：(b) Solve for x: $x = \frac{14}{13}$