Question

Solve the following equations.

20. x/4 + 10 = 3/4
21. 12 = |x + 8|
22. -3|x - 4| + 2 = -7
23. 16(x – 2) – (x – 3) = 29
24.5/6(2x – 8) = 45
25. F = 9/5C + 32 Solve for C.

Answer 1

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Answer 2

20

Start with

`(x)/(4) + 10 = (3)/(4)`

Multiply both sides by 4:

`x+40=3`

Subtract 40 from both sides:

`x = -37`

21

If the absolute value of something equals 12, then that something is either 12 or -12: the possibilities are

`x+8=12 \iff x=4`

or

`x+8=-12 \iff x=-20`

22

You can isolate the absolute value

`-3|x-4|+2=-7 \iff -3|x - 4|=-9 \iff |x - 4|=3`

And proceed as before.

23

Distribute the 16:

`16x-32-x+3=29 \iff 15x-29=29 \iff 15x=58 \iff x = (58)/(15)`

24

Multiply both sides by 6/5:

`2x-8=54 \iff 2x=62 \iff x=31`

25

Start with

`F=(9)/(5)C+32`

Subtract 32 from both sides

`F-32=(9)/(5)C`

Multiply both sides by 5/9

`(5)/(9)(F-32)=C`