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

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

Solve for x

$$x = \frac{11}{4} = 2\frac{3}{4} = 2.75$$

Steps for Solving Linear Equation

Use the distributive property to multiply \frac{1}{2} by x+4.

$$\frac{1}{2}x+\frac{1}{2}\times 4=\frac{3}{4}\left(2x-1\right)$$

Multiply \frac{1}{2} and 4 to get \frac{4}{2}.

$$\frac{1}{2}x+\frac{4}{2}=\frac{3}{4}\left(2x-1\right)$$

Divide 4 by 2 to get 2.

$$\frac{1}{2}x+2=\frac{3}{4}\left(2x-1\right)$$

Use the distributive property to multiply \frac{3}{4} by 2x-1.

$$\frac{1}{2}x+2=\frac{3}{4}\times 2x+\frac{3}{4}\left(-1\right)$$

Express \frac{3}{4}\times 2 as a single fraction.

$$\frac{1}{2}x+2=\frac{3\times 2}{4}x+\frac{3}{4}\left(-1\right)$$

Multiply 3 and 2 to get 6.

$$\frac{1}{2}x+2=\frac{6}{4}x+\frac{3}{4}\left(-1\right)$$

Reduce the fraction \frac{6}{4} to lowest terms by extracting and canceling out 2.

$$\frac{1}{2}x+2=\frac{3}{2}x+\frac{3}{4}\left(-1\right)$$

Multiply \frac{3}{4} and -1 to get -\frac{3}{4}.

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

Subtract \frac{3}{2}x from both sides.

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

Combine \frac{1}{2}x and -\frac{3}{2}x to get -x.

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

Subtract 2 from both sides.

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

Convert 2 to fraction \frac{8}{4}.

$$-x=-\frac{3}{4}-\frac{8}{4}$$

Since -\frac{3}{4} and \frac{8}{4} have the same denominator, subtract them by subtracting their numerators.

$$-x=\frac{-3-8}{4}$$

Subtract 8 from -3 to get -11.

$$-x=-\frac{11}{4}$$

Multiply both sides by -1.

$$x=\frac{11}{4}$$