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Question
Solve: `1/2 ("x" + 5) - 1/3 ("x" - 2) = 4`
Solution
`1/2 ("x" + 5) - 1/3 ("x" - 2) = 4`
Expand `1/2(x+5): 1/2 (x+5) = x/2 + 5/2`
Expand `1/3 (x-2): 1/3 (x-2) = x/3 - 2/3`
The equation becomes: `x/2+5/2-(x/3 - 2/3) = 4.`
Distribute the negative sign across `x/3 - 2/3`
`x/2 + 5/2-x/3+2/3 = 4`
Group the x-terms and constant terms:
`(x/2-x/3)+(5/2+2/3) = 4`
The least common denominator (LCD) of 2 and 3 is 6. Rewrite the x-terms with a denominator of 6: `x/2 = (3x)/6, x/3 = (2x)/6`
`x/2 - x/3 = (3x)/6 - (2x)/6 = x/6`
Simplify the constant terms
`5/2 = 15/6, 2/3 = 4/6`
Add the constant terms:
`5/2+2/3 = 15/6+4/6=19/6`
`x/6+19/6 =4`
`(x+19)/6=4`
Multiply through by 6: x + 19 = 24.
Subtract 19 from both sides: x = 24 − 19 = 5.
x = 5
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