Solve for: (4x)/(3)-2=(2x+3)/(3)-1

Expression: $\frac{ 4x }{ 3 }-2=\frac{ 2x+3 }{ 3 }-1$

Move the expression to the left-hand side and change its sign

$\frac{ 4x }{ 3 }-2-\frac{ 2x+3 }{ 3 }=-1$

Move the constant to the right-hand side and change its sign

$\frac{ 4x }{ 3 }-\frac{ 2x+3 }{ 3 }=-1+2$

Calculate the sum

$\frac{ 4x }{ 3 }-\frac{ 2x+3 }{ 3 }=1$

Multiply both sides of the equation by $3$

$4x-\left( 2x+3 \right)=3$

When there is a $-$ in front of an expression in parentheses, change the sign of each term of the expression and remove the parentheses

$4x-2x-3=3$

Collect like terms

$2x-3=3$

Move the constant to the right-hand side and change its sign

$2x=3+3$

Add the numbers

$2x=6$

Divide both sides of the equation by $2$

$x=3$