Question

4. Solve the equation. Just put the solution without the variable. Solve the equation. 3/4x + 2 - 1/3x = 12

Answer 1

hello

to solve this problem, let's simplify the equation

step 1

collect like terms

`\begin{gathered} (3)/(4)x+2-(1)/(3)x=12 \\ (3)/(4)x-(1)/(3)x=12-2 \\ (3)/(4)x-(1)/(3)x=10 \end{gathered}`

step 2

find the LCM to resolve the fraction

the LCM of 4 and 3 is 12

`\begin{gathered} (3)/(4)x-(1)/(3)x=10 \\ (3(3)-1(4))/(12)x=10 \\ (9-4)/(12)x=10 \\ (5)/(12)x=10 \end{gathered}`

cross multiply and solve for x

`\begin{gathered} (5)/(12)x=10 \\ 5x=10*12 \\ 5x=120 \\ \text{divide both sides by 5} \\ (5x)/(5)=(120)/(5) \\ x=24 \end{gathered}`

x = 24