Solve the equation |7x+5|=40?

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justaguide's profile pic

justaguide | College Teacher | (Level 2) Distinguished Educator

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The absolute value of a number represents only the magnitude of how far it is from 0, whether to the left on the number line or to the right.

This makes |-a| = |a|

We have to solve |7x+5|=40

|7x+5|=40

=> 7x + 5 = 40 and 7x + 5 = -40

=> 7x = 35 and 7x = -45

=> x = 5 and x = -45/7

The solutions of the equation are x = 5 and x = -45/7

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giorgiana1976 | College Teacher | (Level 3) Valedictorian

Posted on

We'll use the property of absolute value to solve this equation:

|7x + 5| = 40 <=> 7x + 5 = 40 , 7x+5 `>=` 0

7x + 5 = -40, 7x+5 < 0

We'll solve the first case:

7x + 5 = 40

7x = 40 - 5

7x = 35

x = 5

Since the values of x must belong to the interval [-5/7,`oo` ), the value x = 5 represents the solution of equation.

We'll solve the 2nd case:

7x + 5 = -40

7x = -45

x = -45/7

Since the values of x must belong to the interval (-` oo` ; -5/7), the value x = -45/7 represents also the solution of equation.

The equation will have two solutions:{-45/7 ; 5}.

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