Answer:
[tex] x = \dfrac{7}{5} [/tex]
Step-by-step explanation:
To solve the equation [tex]2x - 3 = \dfrac{3x - 5}{4}[/tex], we will eliminate the fraction by multiplying both sides of the equation by 4 to clear the denominator. Here are the step-by-step algebraic workings:
Given equation:
[tex] 2x - 3 = \dfrac{3x - 5}{4} [/tex]
Multiply both sides of the equation by 4 to eliminate the fraction:
[tex] 4(2x - 3) = 4 \left( \dfrac{3x - 5}{4} \right) [/tex]
Simplify each side:
[tex] 4(2x - 3) = 3x - 5 [/tex]
Expand the left side:
[tex] 8x - 12 = 3x - 5 [/tex]
Now, isolate the variable [tex]x[/tex] by moving all terms involving [tex]x[/tex] to one side and constants to the other side:
Subtract [tex]3x[/tex] from both sides:
[tex] 8x - 12 - 3x = -5 [/tex]
Simplify the left side:
[tex] 5x - 12 = -5 [/tex]
Add 12 to both sides to isolate [tex]5x[/tex]:
[tex] 5x - 12 + 12 = -5 + 12 [/tex]
Simplify:
[tex] 5x = 7 [/tex]
Finally, solve for [tex]x[/tex] by dividing both sides by 5:
[tex] \dfrac{5x}{5} = \dfrac{7}{5} [/tex]
Simplify:
[tex] x = \dfrac{7}{5} [/tex]
Therefore, the solution to the equation is:
[tex] \boxed{x = \dfrac{7}{5}} [/tex]
