Question

Solve each absolute value equation
-4[x] + 10 = 50

Answer 1

Explanation:

`\bf \underline{Given-} \\`

`\sf{ - 4(x) + 10 = 50} \\`

`\bf \underline{To \: find-} \\`

`\sf{ \:the \: value \: of \: x = \: ? } \\`

`\bf \underline{Solution-} \\`

`\textsf{Given equation,}\\`

`\sf{ - 4(x) + 10 = 50} \\`

• Now, multiply -4 from (x) to get -4x.

`\sf{ \Rightarrow \: - 4x + 10 = 50 } \\`

• Now, +10 will move to RHS then it's sign will be charged -10

`\sf{ \Rightarrow \: - 4x = 50 - 10} \\`

• Subtract 50 from -10 to get 40. Because 50 is greater than -10.

`\sf{ \Rightarrow \: - 4x = 40 } \\`

`\sf{ \Rightarrow \: x = \cancel\frac{ - {40}^(- 10 )}{4}} \\`

`{ \: \therefore \: \underline{ \boxed{{ \sf{x = - 10.}}}}}`

Answer 2

`\large\boxed{\mathsf{-4[x] + 10 = 50}}\\\large\boxed{\rightarrow\mathsf{-4x + 10 = 50}}\\\\\large\text{SUBTRACT 10 to BOTH SIDES}\\\large\boxed{\mathsf{-4x + 10 - 10 = 50 - 10}}\\\large\text{CANCEL out: 10 - 10 because that gives you 0}\\\large\text{KEEP: 50 - 10 because it helps solve for the x-value}\\\\\large\boxed{\mathsf{50 - 10 = \bf 40}}\\\large\boxed{\mathsf{-4x = 40}}\\\\\large\text{DIVIDE -4 to BOTH SIDES}\\\large\boxed{\mathsf{(-4x)/(4)=(40)/(-4)}}`

`\large\text{CANCEL out: }\rm{(-4)/(-4)}\large\text{ because that gives you 1}\\\large\text{KEEP: }\rm{(40)/(-4)}\large\text{ because it gives you the x-value answer}\\\\\large\boxed{\mathsf{x = (40)/(-4)}}\\\\\large\text{SIMPLIFY IT AND YOU HAVE THE RESULT OF THE X! }\\\\\huge\boxed{\text{Therefore, your answer is: \textsf{x = -10}}}\huge\checkmark`