Solve 5-2x=1/7(2x+3)

$$5 - 2 x = \frac { 1 } { 7 } ( 2 x + 3 )$$

Solve for x

$$x=2$$

Steps for Solving Linear Equation

Use the distributive property to multiply \frac{1}{7} by 2x+3.

$$5-2x=\frac{1}{7}\times 2x+\frac{1}{7}\times 3$$

Multiply \frac{1}{7} and 2 to get \frac{2}{7}.

$$5-2x=\frac{2}{7}x+\frac{1}{7}\times 3$$

Multiply \frac{1}{7} and 3 to get \frac{3}{7}.

$$5-2x=\frac{2}{7}x+\frac{3}{7}$$

Subtract \frac{2}{7}x from both sides.

$$5-2x-\frac{2}{7}x=\frac{3}{7}$$

Combine -2x and -\frac{2}{7}x to get -\frac{16}{7}x.

$$5-\frac{16}{7}x=\frac{3}{7}$$

Subtract 5 from both sides.

$$-\frac{16}{7}x=\frac{3}{7}-5$$

Convert 5 to fraction \frac{35}{7}.

$$-\frac{16}{7}x=\frac{3}{7}-\frac{35}{7}$$

Since \frac{3}{7} and \frac{35}{7} have the same denominator, subtract them by subtracting their numerators.

$$-\frac{16}{7}x=\frac{3-35}{7}$$

Subtract 35 from 3 to get -32.

$$-\frac{16}{7}x=-\frac{32}{7}$$

Multiply both sides by -\frac{7}{16}, the reciprocal of -\frac{16}{7}.

$$x=-\frac{32}{7}\left(-\frac{7}{16}\right)$$

Multiply -\frac{32}{7} times -\frac{7}{16} by multiplying numerator times numerator and denominator times denominator.

$$x=\frac{-32\left(-7\right)}{7\times 16}$$

Do the multiplications in the fraction \frac{-32\left(-7\right)}{7\times 16}.

$$x=\frac{224}{112}$$

Divide 224 by 112 to get 2.

$$x=2$$