Solve for x
x=8
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2\left(x+7\right)+3\left(x-8\right)=6x-18
Multiply both sides of the equation by 6, the least common multiple of 3,2.
2x+14+3\left(x-8\right)=6x-18
Use the distributive property to multiply 2 by x+7.
2x+14+3x-24=6x-18
Use the distributive property to multiply 3 by x-8.
5x+14-24=6x-18
Combine 2x and 3x to get 5x.
5x-10=6x-18
Subtract 24 from 14 to get -10.
5x-10-6x=-18
Subtract 6x from both sides.
-x-10=-18
Combine 5x and -6x to get -x.
-x=-18+10
Add 10 to both sides.
-x=-8
Add -18 and 10 to get -8.
x=8
Multiply both sides by -1.
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