Home > Algebra > Absolute Value Equations

How do you solve the equation #4-absx=2x+1#?

Answer 1

#x=1#

If #x>=0# then we have #4-x=2x+1# so we get #x=1# If #x<0# then we have #4+x=2x+1# so #x=3# This is impossible, since we have assumed that #x<0#

By signing up, you agree to our Terms of Service and Privacy Policy

Answer 2

Eva Abramson

To solve the equation (4 - |x| = 2x + 1), follow these steps:

Split the equation into two cases based on the absolute value:

Case 1: (x \geq 0) Case 2: (x < 0)
For Case 1 ((x \geq 0)), the absolute value (|x|) is equal to (x), so rewrite the equation as (4 - x = 2x + 1) and solve for (x).
For Case 2 ((x < 0)), the absolute value (|x|) is equal to (-x), so rewrite the equation as (4 + x = 2x + 1) and solve for (x).
Check the solutions obtained in Steps 2 and 3 to ensure they satisfy the original equation.

After solving both cases, you'll get the values of (x) that satisfy the equation.

By signing up, you agree to our Terms of Service and Privacy Policy

Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.