In Exercises 61–66, find all values of x satisfying the given conditions. y1=x−35,y2=x−54,andy1−y2=1y_1 = \frac{x - 3}{5}, \quad $$y_2$$ = \frac{x - 5}{4}, \quad \text{and} \quad $$y_1$$ - $$y_2 = 1 y1$$=5x−3,y2=4x−5,andy1−y2=1

Ch. 1 - Equations and Inequalities

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Blitzer 8th Edition

Ch. 1 - Equations and Inequalities

Problema 63

Capitolo 2, Problema 63

In Exercises 61–66, find all values of x satisfying the given conditions. $y_1 = $\frac{x - 3}{5}$, $\quad$ y_2 = $\frac{x - 5}{4}$, $\quad$ $\text{and}$ $\quad$ y_1 - y_2 = 1$

Guida verificata passo dopo passo

Start by writing down the given equations: $ y_1 = \frac{x - 3}{5} $, $ y_2 = \frac{x - 5}{4} $, and the condition $ y_1 - y_2 = 1 $.

Substitute the expressions for $ y_1 $ and $ y_2 $ into the equation $ y_1 - y_2 = 1 $ to get: $ \frac{x - 3}{5} - \frac{x - 5}{4} = 1 $.

Find a common denominator for the fractions on the left side, which is 20, and rewrite the equation as: $ \frac{4(x - 3)}{20} - \frac{5(x - 5)}{20} = 1 $.

Combine the fractions over the common denominator: $ \frac{4(x - 3) - 5(x - 5)}{20} = 1 $.

Multiply both sides of the equation by 20 to eliminate the denominator, then simplify and solve the resulting linear equation for $ x $.

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