Question

Please help me with my math hw

Answer 1

See below for answers and explanations

Explanation:

Problem 1

`(3)/(4)x=60\\ \\(3)/(4)x*4=60*4\\ \\3x=240\\\\(3x)/(3)=(240)/(3)\\ \\ x=80`

Check solution:

`(3)/(4)(80)\stackrel{?}{=}60\\\\(3*80)/(4)\stackrel{?}{=}60\\\\(240)/(4)\stackrel{?}{=}60\\\\60=60`

Problem 2

`(2)/(5)x=42\\ \\(2)/(5)x*5=42*5\\ \\2x=210\\\\(2x)/(2)=(210)/(2)\\ \\ x=105`

Check solution:

`(2)/(5)(105)\stackrel{?}{=}42\\\\(2*105)/(5)\stackrel{?}{=}42\\ \\(210)/(5)\stackrel{?}{=}42\\ \\42=42`

Problem 3

`(3)/(5)y=40\\ \\(3)/(5)y*5=40*5\\ \\3y=200\\\\(3y)/(3)=(200)/(3)\\ \\ y=(200)/(3)`

Check solution:

`(3)/(5)((200)/(3))\stackrel{?}{=} 40\\ \\ (3*200)/(5*3)\stackrel{?}{=} 40\\ \\(600)/(15)\stackrel{?}{=}40\\\\40=40`

Problem 4

`-(8)/(3)m=6\\\\-(8)/(3)m*3=6*3\\ \\-8m=18\\\\(-8m)/(-8)=(18)/(-8)\\\\m=-(18)/(8)\\ \\m=-(9)/(4)`

Check solution:

`-(8)/(3)(-(9)/(4))\stackrel{?}{=}6\\\\(-8*-9)/(3*4)\stackrel{?}{=}6\\\\(72)/(12)\stackrel{?}{=}6\\ \\6=6`

Problem 5

`(5)/(6)x=4\\ \\(5)/(6)x*6=4*6\\ \\5x=24\\\\(5x)/(5)=(24)/(5)\\ \\ x=(24)/(5)`

Check solution:

`(5)/(6)((24)/(5))\stackrel{?}{=}4\\ \\(5*24)/(6*5)\stackrel{?}{=}4\\\\(24)/(6)\stackrel{?}{=}4\\ \\4=4`

Problem 6

`(5)/(3)x=12\\ \\(5)/(3)x*3=12*3\\ \\5x=36\\\\(5x)/(5)=(36)/(5)\\ \\x=(36)/(5)`

Check solution:

`(5)/(3)((36)/(5))\stackrel{?}{=}12\\\\(5*36)/(3*5)\stackrel{?}{=}12\\ \\(36)/(3)\stackrel{?}{=}12\\ \\12=12`