Solve -5/2(-4+3x)=1-3/4(3x+4)

$$- \frac { 5 } { 2 } ( - 4 + 3 x ) = 1 - \frac { 3 } { 4 } ( 3 x + 4 )$$

Solve for x

$$x = \frac{16}{7} = 2\frac{2}{7} \approx 2.285714286$$

Steps for Solving Linear Equation

Use the distributive property to multiply -\frac{5}{2} by -4+3x.

$$-\frac{5}{2}\left(-4\right)-\frac{5}{2}\times 3x=1-\frac{3}{4}\left(3x+4\right)$$

Express -\frac{5}{2}\left(-4\right) as a single fraction.

$$\frac{-5\left(-4\right)}{2}-\frac{5}{2}\times 3x=1-\frac{3}{4}\left(3x+4\right)$$

Multiply -5 and -4 to get 20.

$$\frac{20}{2}-\frac{5}{2}\times 3x=1-\frac{3}{4}\left(3x+4\right)$$

Divide 20 by 2 to get 10.

$$10-\frac{5}{2}\times 3x=1-\frac{3}{4}\left(3x+4\right)$$

Express -\frac{5}{2}\times 3 as a single fraction.

$$10+\frac{-5\times 3}{2}x=1-\frac{3}{4}\left(3x+4\right)$$

Multiply -5 and 3 to get -15.

$$10+\frac{-15}{2}x=1-\frac{3}{4}\left(3x+4\right)$$

Fraction \frac{-15}{2} can be rewritten as -\frac{15}{2} by extracting the negative sign.

$$10-\frac{15}{2}x=1-\frac{3}{4}\left(3x+4\right)$$

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

$$10-\frac{15}{2}x=1-\frac{3}{4}\times 3x-\frac{3}{4}\times 4$$

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

$$10-\frac{15}{2}x=1+\frac{-3\times 3}{4}x-\frac{3}{4}\times 4$$

Multiply -3 and 3 to get -9.

$$10-\frac{15}{2}x=1+\frac{-9}{4}x-\frac{3}{4}\times 4$$

Fraction \frac{-9}{4} can be rewritten as -\frac{9}{4} by extracting the negative sign.

$$10-\frac{15}{2}x=1-\frac{9}{4}x-\frac{3}{4}\times 4$$

Cancel out 4 and 4.

$$10-\frac{15}{2}x=1-\frac{9}{4}x-3$$

Subtract 3 from 1 to get -2.

$$10-\frac{15}{2}x=-2-\frac{9}{4}x$$

Add \frac{9}{4}x to both sides.

$$10-\frac{15}{2}x+\frac{9}{4}x=-2$$

Combine -\frac{15}{2}x and \frac{9}{4}x to get -\frac{21}{4}x.

$$10-\frac{21}{4}x=-2$$

Subtract 10 from both sides.

$$-\frac{21}{4}x=-2-10$$

Subtract 10 from -2 to get -12.

$$-\frac{21}{4}x=-12$$

Multiply both sides by -\frac{4}{21}, the reciprocal of -\frac{21}{4}.

$$x=-12\left(-\frac{4}{21}\right)$$

Express -12\left(-\frac{4}{21}\right) as a single fraction.

$$x=\frac{-12\left(-4\right)}{21}$$

Multiply -12 and -4 to get 48.

$$x=\frac{48}{21}$$

Reduce the fraction \frac{48}{21} to lowest terms by extracting and canceling out 3.

$$x=\frac{16}{7}$$