solve and check 2|5x-10|+17=37

Question

i dont understand the algebra problem.

Answer 1

The equation is 2|5x-10| + 17 = 37 .

First rewrite the above equation in the form |ax+b| = c where c = ≥0 and it is equivalent to the statement  ax+b = c or ax+b = - c.

Subtract 17 from each side.

2|5x-10| = 20

Divide each side by 2.

|5x-10| = 10.

Rewrite the equation |5x-10| = 10 as two equations .

5x-10 = 10 or 5x-10 = -10 Then solve each equation separately.

Solve the equation 1: 5x-10 = 10

Add 10 to each side.

5x = 20

Divide each side by 5.

x = 20/5

x = 4.

Solve the equation 2: 5x-10 = -10.

Add 10 to each side.

5x = 0

x = 0.

Check:-

To check the solution, substitute the value of x = 4 in the original equation.

2|5(4) -10| + 17 = 37

2|20 -10| + 17 = 37

2|10| + 17 = 37

20 + 17 = 37

37 = 37

The above statement is true, so the value of x = 4 in the solution of the original equation.

Check:-

To check the solution, substitute the value of x = 0 in the original equation.

2|5(0) -10| + 17 = 37

2|-10| + 17 = 37

20 + 17 = 37

37 = 37

The above statement is true, so the value of x = 0 in the solution of the original equation.