Answer:
[tex] \boxed{ \bold{ \boxed{ \sf{1. \: \: \: \: \: x = 12}}}}[/tex]
[tex] \boxed{ \bold{ \boxed{ \sf{2. \: \: \: \: \: x = 3}}}}[/tex]
Step-by-step explanation:
[tex] \sf{1. \: \: \: \: \frac{x}{3} + 2 = \frac{x}{4} + 3}[/tex]
Move x / 4 to left hand side and change its sign
Similarly, move 2 to right hand side and change it's sign
[tex] \longrightarrow{ \sf{ \frac{x}{3} - \frac{x}{4} = 3 - 2}}[/tex]
Take the L.C.M of 3 and 4
L.C.M of 3 and 4 = 12
[tex] \longrightarrow{ \sf{ \frac{x \times 4 - x \times 3}{12} = 3 - 2}}[/tex]
[tex] \longrightarrow{ \sf{ \frac{4x - 3x}{12} = 3 - 2}}[/tex]
[tex] \longrightarrow{ \sf{ \frac{x}{12} = 3 - 2}}[/tex]
Subtract 2 from 3
[tex] \longrightarrow{ \sf{ \frac{x}{12} = 1}}[/tex]
Do cross multiplication
[tex] \longrightarrow{ \sf{x = 1 \times 12}}[/tex]
[tex] \longrightarrow { \sf{x = 12}}[/tex]
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[tex] \sf{2. \: \: \: \: 3(4 + 2x) = 33 - x }[/tex]
Distribute 3 through the parentheses
[tex] \longrightarrow{ \sf{12 + 6x = 33 - x}}[/tex]
Move x to left hand side and change it's sign
Similarly, move 12 to right hand side and change it's sign
[tex] \longrightarrow{ \sf{6x + x = 33 - 12}}[/tex]
Collect like terms
[tex] \longrightarrow{ \sf{7x = 33 - 12}}[/tex]
Subtract 12 from 33
[tex] \longrightarrow{ \sf{7x = 21}}[/tex]
Divide both sides by 7
[tex] \longrightarrow{ \sf{ \frac{7x}{7} = \frac{21}{7} }}[/tex]
Calculate
[tex] \longrightarrow{ \sf{x = 3}}[/tex]
Hope I helped!
Best regards! :D
