Question

tìm x biết |x+1|+|x+2|+|x+3|=4x

Answer 1

Ta có : |x+1| \(\ge\)0; |x+2|\(\ge\)0;|x+3|\(\ge\)0

=> |x+1| + |x+2| + |x+3|\(\ge\)0

=> 4x \(\ge\)0 => x\(\ge\)0

=> x+1 \(\ge\)0; x+2 \(\ge\)0; x + 3\(\ge\)0

=> |x+1| = x + 1 ; |x+2| = x + 2 ; |x+.3| = x + 3

=> (x+1) + (x+2) + (x+3) = 4x

=> 3x + 6 = 4x

=> 1x = 6

=> x = 6

Answer 2

Ta có : |x+1| ≥≥0; |x+2|≥≥0;|x+3|≥≥0

=> |x+1| + |x+2| + |x+3|≥≥0

=> 4x ≥≥0 => x≥≥0

=> x+1 ≥≥0; x+2 ≥≥0; x + 3≥≥0

=> |x+1| = x + 1 ; |x+2| = x + 2 ; |x+.3| = x + 3

=> (x+1) + (x+2) + (x+3) = 4x

=> 3x + 6 = 4x

=> 1x = 6

=> x = 6