How do you solve |-4x + 10| ≤ 46?

2 Answers

The solution is
For all values above 9 and less than or equal to 14, the relation is valid

Explanation:

abs(-4x+10)<=46
-4x+10<=46
-4x<=46-10
-4x<=36
-x<=36/4
-x<=9
x>9
or
-4x+10<=-46
-4x<=-46-10
-4x<=-56
4x<=56
x<=56/4
x<=14
The solution is
x>9,x<=14
For all values above 9 and less than or equal to 14, the relation is valid

Aug 6, 2018

The solution is x in [-9,14]

Explanation:

The inequality is

|-4x+10|<=46

The solution is

{(4x-10<=46),(-4x+10<=46):}

<=>, {(4x<=46+10),(4x>=10-46):}

<=>, {(4x<=56),(4x>=-36):}

<=>, {(x<=56/4),(x>=-36/4):}

<=>, {(x<=14),(x>=-9):}

The solution is

x in [-9,14]

graph{|4x-10|-46 [-105.4, 105.4, -52.7, 52.7]}