Question

solve and write using set builder notation. 12-8(3x-5)>-7x+29

Answer 1

\[\Large12-8\left( 3x-5\right)>-7x+29\]

multiply out: -8(3x-5)
\[-8(3x-5) =-24x+40\]
\[\implies\Large12-24x+40>-7x+29\]\[\implies\Large-24x+52>-7x+29\]

Next, bring all the x-terms on one side and all the no-x-terms to the other side: \[\implies\Large52-29>-7x+24x\]\[\implies\Large23>17x\]

Lastly divide both sides by 17\[\huge \therefore{23\over17}>x\]
or \[\huge x<{23\over17}\]

in set notation:
\[\huge \left\{ x \in \mathbb{R}:x<{23 \over7} \right\}\]

Answer 2

Ok, Thank You wanted to check my answer.