Math  /  Algebra

QuestionSolve for xx in each equation, assuming a0a \neq 0:
1. 4=ax144 = a x - 14
2. ax5=19a x - 5 = 19
3. 6+ax=296 + a x = -29
4. 8ax5=3\frac{8}{a x} - 5 = -3
5. 18ax=4218 - a x = 42

Studdy Solution
Assumptions1. The variable aa is a constant and a0a \neq0. . The variable xx is the unknown we want to solve for.
Problem19We start by isolating axax on one side of the equation. We do this by adding14 to both sides of the equation.
4+14=ax14+144 +14 = ax -14 +143implify the equation.
ax=18ax =184Finally, we solve for xx by dividing both sides of the equation by aa.
x=18ax = \frac{18}{a}Problem205We start by isolating axax on one side of the equation. We do this by adding5 to both sides of the equation.
ax5+5=19+5ax -5 +5 =19 +56implify the equation.
ax=24ax =247Finally, we solve for xx by dividing both sides of the equation by aa.
x=24ax = \frac{24}{a}Problem218We start by isolating axax on one side of the equation. We do this by subtracting6 from both sides of the equation.
6+ax6=2966 + ax -6 = -29 -69implify the equation.
ax=35ax = -3510Finally, we solve for xx by dividing both sides of the equation by aa.
x=35ax = \frac{-35}{a}Problem2211We start by isolating axax on one side of the equation. We do this by adding5 to both sides of the equation.
8ax5+5=3+5\frac{8}{ax} -5 +5 = -3 +512implify the equation.
8ax=\frac{8}{ax} =13To get rid of the fraction, we multiply both sides of the equation by axax.
8=ax8 =ax14Finally, we solve for xx by dividing both sides of the equation by aa.
x=8ax = \frac{8}{a}15implify the equation.
x=4ax = \frac{4}{a}Problem2316We start by isolating axax on one side of the equation. We do this by subtracting18 from both sides of the equation.
18ax18=421818 - ax -18 =42 -1817implify the equation.
ax=24-ax =2418Finally, we solve for xx by dividing both sides of the equation by a-a.
x=24ax = \frac{24}{-a}19implify the equation.
x=24ax = \frac{-24}{a}

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