Question

1.`1/2t+36=-5?" "` 2. Solve for `q:(5q-3n)/m=f" "`3.Two numbers add up to `157` and the first is `17` bigger than the second. What is are the two numbers? `" "`4.Solve `3x-2=4(x-1)+2x" "` 5.Solve for r:`" "A=2 pi " radius " h`

Answer 1

1. `t=-82`
2. `q = (fm+3n)/5" " or q= (fm)/5 +(3n)/5`
3. The numbers are `120 and 137`
4. `x =2/3`
5. `r = A/(2pih)`

Explanation:

1. Solve for `t`

`1/2 t+36 -36 = -5-36" "larr` subtract 36 from both sides
`1/2t = -41`

`(cancel2xx1)/cancel2t = 2xx-41" "larr` multiply both sides by `2`
`t =-82`
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2. Make `q` the subject

`(5q-3n)/m=f" "larr` multiply by #m

`5q -3n = fm`

`5q = fm +3n" "larr` add `3n` to both sides

`q = (fm+3n)/5" " or (fm)/5 +(3n)/5`
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3. Let the smaller number be `x`
The larger number is `17` more, so it will be `x+17`

`x+x+17 = 257" "larr` their sum is `157`

`2x = 240" "larr` subtract 17 from both sides

`x = 120`

The numbers are `120 and 137`
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4. `" "3x-2=4(x-1)+2x" "larr` remove the brackets

`3x-2 = 4x-4+2x" "larr` keep the `x` terms on the right

`-2+4 = 6x-3x`

`2 = 3x" "larr` divide by `3`

`2/3 =x`
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5. Make `r` the subject in `A = 2 pi rh`

`2pirh = A" "larr` divide both sides by `2pih`

`r = A/(2pih)`