Solve the equation check for extraneous solutions
9[9-8x]=2x+3
please explain
81 - 72x = 2x + 3
78 = 70x
x = 78/70 = 39/35
To solve the given equation, we will follow the steps outlined below:
Step 1: Simplify both sides of the equation by distributing the 9 on the left-hand side:
81 - 72x = 2x + 3
Step 2: Rearrange the equation to bring the variable terms on one side and the constant terms on the other side:
-72x - 2x = 3 - 81
Step 3: Combine like terms:
-74x = -78
Step 4: Divide both sides of the equation by -74 to isolate the variable x:
x = -78 / -74
Step 5: Simplify the fraction:
x ≈ 1.054
Now, to check for extraneous solutions, we substitute x = 1.054 back into the original equation and see if both sides are equal:
Left-hand side:
9[9 - 8(1.054)] = 9[9 - 8.432] = 9(0.568) ≈ 5.112
Right-hand side:
2(1.054) + 3 = 2.108 + 3 ≈ 5.108
The values on both sides are approximately equal (5.112 ≈ 5.108), which means there are no extraneous solutions in this case. Thus, the solution to the equation is x ≈ 1.054.